Nuprl Lemma : Kan-cubical-type_wf
∀[X:CubicalSet]. ({X ⊢ _(Kan)} ∈ 𝕌')
Proof
Definitions occuring in Statement :
Kan-cubical-type: {X ⊢ _(Kan)},
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,
Kan-cubical-type: {X ⊢ _(Kan)},
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
uimplies: b supposing a,
nameset: nameset(L),
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
cubical-type_wf,
list_wf,
coordinate_name_wf,
I-cube_wf,
nameset_wf,
int_seg_wf,
A-open-box_wf,
subtype_rel_list,
cubical-type-at_wf,
Kan-A-filler_wf,
uniform-Kan-A-filler_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
functionEquality,
applyEquality,
lambdaEquality,
cumulativity,
universeEquality,
because_Cache,
natural_numberEquality,
dependent_functionElimination,
independent_isectElimination,
setElimination,
rename,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:CubicalSet]. (\{X \mvdash{} \_(Kan)\} \mmember{} \mBbbU{}')
Date html generated:
2016_06_16-PM-06_44_01
Last ObjectModification:
2015_12_28-PM-04_25_46
Theory : cubical!sets
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