Nuprl Lemma : canonical-section_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[I:fset(ℕ)]. ∀[rho:Gamma(I)]. ∀[a:A(rho)].
(canonical-section(Gamma;A;I;rho;a) ∈ {formal-cube(I) ⊢ _:(A)<rho>})
Proof
Definitions occuring in Statement :
canonical-section: canonical-section(Gamma;A;I;rho;a),
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
context-map: <rho>,
formal-cube: formal-cube(I),
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube-cat: CubeCat,
all: ∀x:A. B[x],
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a),
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
context-map: <rho>,
ps-context-map: <rho>,
formal-cube: formal-cube(I),
Yoneda: Yoneda(I),
canonical-section: canonical-section(Gamma;A;I;rho;a),
ps-canonical-section: ps-canonical-section(Gamma;A;I;rho;a),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f)
Lemmas referenced :
ps-canonical-section_wf,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
cat_comp_tuple_lemma,
cubical-term-sq-presheaf-term
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop,
dependent_functionElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[rho:Gamma(I)]. \mforall{}[a:A(rho)].
(canonical-section(Gamma;A;I;rho;a) \mmember{} \{formal-cube(I) \mvdash{} \_:(A)<rho>\})
Date html generated:
2020_05_20-PM-01_53_17
Last ObjectModification:
2020_04_03-PM-08_28_09
Theory : cubical!type!theory
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