Nuprl Lemma : csm-closed-type
∀[T:{ * ⊢ _}]. ∀[s:Top]. ((closed-type-to-type(T))s ~ closed-type-to-type(T))
Proof
Definitions occuring in Statement :
closed-type-to-type: closed-type-to-type(T),
closed-cubical-type: { * ⊢ _},
csm-ap-type: (AF)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
closed-cubical-type: { * ⊢ _},
csm-ap-type: (AF)s,
closed-type-to-type: closed-type-to-type(T)
Lemmas referenced :
istype-top,
closed-cubical-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
hypothesis,
axiomSqEquality,
extract_by_obid,
isect_memberEquality_alt,
isectElimination,
hypothesisEquality,
isectIsTypeImplies,
inhabitedIsType,
universeIsType
Latex:
\mforall{}[T:\{ * \mvdash{} \_\}]. \mforall{}[s:Top]. ((closed-type-to-type(T))s \msim{} closed-type-to-type(T))
Date html generated:
2020_05_20-PM-01_51_05
Last ObjectModification:
2020_03_20-AM-11_39_59
Theory : cubical!type!theory
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