Nuprl Lemma : cubical-type_wf
∀[X:CubicalSet]. (X ⊢ ∈ 𝕌')
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-type: {X ⊢ _},
subtype_rel: A ⊆r B,
and: P ∧ Q,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
list_wf,
coordinate_name_wf,
I-cube_wf,
name-morph_wf,
cube-set-restriction_wf,
all_wf,
equal_wf,
id-morph_wf,
subtype_rel-equal,
squash_wf,
true_wf,
cube-set-restriction-id,
iff_weakening_equal,
name-comp_wf,
cube-set-restriction-comp,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
productEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
because_Cache,
functionExtensionality,
productElimination,
independent_isectElimination,
instantiate,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
dependent_functionElimination,
axiomEquality
Latex:
\mforall{}[X:CubicalSet]. (X \mvdash{} \mmember{} \mBbbU{}')
Date html generated:
2017_10_05-AM-10_12_26
Last ObjectModification:
2017_07_28-AM-11_18_17
Theory : cubical!sets
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