Nuprl Lemma : context-map-ap-type
∀[I:fset(ℕ)]. ∀[Gamma:j⊢]. ∀[rho:Gamma(I)]. ∀[A:{Gamma ⊢ _}]. formal-cube(I) ⊢ (A)<rho>
Proof
Definitions occuring in Statement :
csm-ap-type: (AF)s,
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,
cube-cat: CubeCat,
all: ∀x:A. B[x],
cubical_set: CubicalSet,
I_cube: A(I),
I_set: A(I),
formal-cube: formal-cube(I),
Yoneda: Yoneda(I),
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>
Lemmas referenced :
ps-context-map-ap-type,
cube-cat_wf,
cat_ob_pair_lemma,
cubical-type-sq-presheaf-type,
cat_arrow_triple_lemma,
cat_comp_tuple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
dependent_functionElimination,
Error :memTop
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[Gamma:j\mvdash{}]. \mforall{}[rho:Gamma(I)]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. formal-cube(I) \mvdash{} (A)<rho>
Date html generated:
2020_05_20-PM-01_49_32
Last ObjectModification:
2020_04_03-PM-08_27_01
Theory : cubical!type!theory
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