Nuprl Lemma : type-csm-Kan-cubical-type
∀[Gamma:CubicalSet]. ∀[s:Top]. ∀[AK:{Gamma ⊢ _(Kan)}]. (Kan-type((AK)s) ~ (Kan-type(AK))s)
Proof
Definitions occuring in Statement :
csm-Kan-cubical-type: (AK)s,
Kan-type: Kan-type(Ak),
Kan-cubical-type: {X ⊢ _(Kan)},
csm-ap-type: (AF)s,
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Kan-cubical-type: {X ⊢ _(Kan)},
Kan-type: Kan-type(Ak),
csm-Kan-cubical-type: (AK)s,
pi1: fst(t)
Lemmas referenced :
Kan-cubical-type_wf,
top_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
hypothesis,
sqequalAxiom,
lemma_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[Gamma:CubicalSet]. \mforall{}[s:Top]. \mforall{}[AK:\{Gamma \mvdash{} \_(Kan)\}]. (Kan-type((AK)s) \msim{} (Kan-type(AK))s)
Date html generated:
2016_06_16-PM-06_45_22
Last ObjectModification:
2015_12_28-PM-04_25_15
Theory : cubical!sets
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