Nuprl Lemma : Kan-type_wf
∀[X:CubicalSet]. ∀[AK:{X ⊢ _(Kan)}]. X ⊢ Kan-type(AK)
Proof
Definitions occuring in Statement :
Kan-type: Kan-type(Ak),
Kan-cubical-type: {X ⊢ _(Kan)},
cubical-type: {X ⊢ _},
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Kan-type: Kan-type(Ak),
Kan-cubical-type: {X ⊢ _(Kan)},
pi1: fst(t)
Lemmas referenced :
Kan-cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[AK:\{X \mvdash{} \_(Kan)\}]. X \mvdash{} Kan-type(AK)
Date html generated:
2016_06_16-PM-06_44_12
Last ObjectModification:
2015_12_28-PM-04_25_36
Theory : cubical!sets
Home
Index