Nuprl Lemma : cubical-path-app_wf
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[a,b:{X ⊢ _:A}]. ∀[t:{X ⊢ _:(Path_A a b)}]. ∀[r:{X ⊢ _:𝕀}]. (t @ r ∈ {X ⊢ _:A})
Proof
Definitions occuring in Statement :
cubical-path-app: pth @ r,
path-type: (Path_A a b),
interval-type: 𝕀,
cubical-term: {X ⊢ _: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,
cubical-path-app: pth @ r,
subtype_rel: A ⊆r B
Lemmas referenced :
cubicalpath-app_wf,
path-type-subtype,
cubical-term_wf,
interval-type_wf,
path-type_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
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,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
instantiate,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[a,b:\{X \mvdash{} \_:A\}]. \mforall{}[t:\{X \mvdash{} \_:(Path\_A a b)\}]. \mforall{}[r:\{X \mvdash{} \_:\mBbbI{}\}].
(t @ r \mmember{} \{X \mvdash{} \_:A\})
Date html generated:
2020_05_20-PM-03_16_40
Last ObjectModification:
2020_04_06-PM-06_31_59
Theory : cubical!type!theory
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