Nuprl Lemma : pathtype_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. X ⊢ Path(A)
Proof
Definitions occuring in Statement :
pathtype: Path(A),
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,
pathtype: Path(A)
Lemmas referenced :
cubical-fun_wf,
interval-type_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. X \mvdash{} Path(A)
Date html generated:
2020_05_20-PM-03_14_03
Last ObjectModification:
2020_04_06-PM-05_17_37
Theory : cubical!type!theory
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