Nuprl Lemma : ctt-type-comp_wf
∀[X:⊢''']. ∀[T:cttType(X)]. (comp(T) ∈ Comp(X;level(T);type(T)))
Proof
Definitions occuring in Statement :
ctt-type-comp: comp(T),
ctt-type-type: type(T),
ctt-type-level: level(T),
ctt-type-meaning: cttType(X),
ctt-level-comp: Comp(X;lvl;T),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-type-meaning: cttType(X),
ctt-type-comp: comp(T),
ctt-type-type: type(T),
ctt-type-level: level(T),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
ctt-type-meaning_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
instantiate
Latex:
\mforall{}[X:\mvdash{}''']. \mforall{}[T:cttType(X)]. (comp(T) \mmember{} Comp(X;level(T);type(T)))
Date html generated:
2020_05_20-PM-07_58_21
Last ObjectModification:
2020_05_07-AM-11_38_11
Theory : cubical!type!theory
Home
Index