Nuprl Lemma : ctt-type-level_wf
∀[X:⊢''']. ∀[T:cttType(X)]. (level(T) ∈ ℕ4)
Proof
Definitions occuring in Statement :
ctt-type-level: level(T),
ctt-type-meaning: cttType(X),
cubical_set: CubicalSet,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-type-level: level(T),
ctt-type-meaning: cttType(X)
Lemmas referenced :
pi1_wf_top,
int_seg_wf,
ctt-type-meaning_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
productElimination,
independent_pairEquality,
hypothesisEquality,
Error :memTop,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate
Latex:
\mforall{}[X:\mvdash{}''']. \mforall{}[T:cttType(X)]. (level(T) \mmember{} \mBbbN{}4)
Date html generated:
2020_05_20-PM-07_57_03
Last ObjectModification:
2020_05_05-PM-05_22_42
Theory : cubical!type!theory
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