Nuprl Lemma : cubical-type_wf
∀[X:j⊢]. (X ⊢ ∈ 𝕌{[i' | j']})
Proof
Definitions occuring in Statement :
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
cubical-type: {X ⊢ _},
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
fset_wf,
nat_wf,
I_cube_wf,
names-hom_wf,
cube-set-restriction_wf,
equal_wf,
nh-id_wf,
subtype_rel-equal,
squash_wf,
true_wf,
istype-universe,
cube-set-restriction-id,
subtype_rel_self,
iff_weakening_equal,
nh-comp_wf,
cube-set-restriction-comp,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
setEquality,
productEquality,
functionEquality,
cumulativity,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
instantiate,
hypothesisEquality,
universeEquality,
applyEquality,
spreadEquality,
independent_isectElimination,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
axiomEquality
Latex:
\mforall{}[X:j\mvdash{}]. (X \mvdash{} \mmember{} \mBbbU{}\{[i' | j']\})
Date html generated:
2020_05_20-PM-01_46_09
Last ObjectModification:
2020_03_24-AM-10_01_12
Theory : cubical!type!theory
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