Nuprl Lemma : cc-adjoin-cube_wf
∀X:j⊢. ∀A:{X ⊢ _}. ∀J:fset(ℕ). ∀v:X(J). ∀u:A(v). ((v;u) ∈ X.A(J))
Proof
Definitions occuring in Statement :
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
cube-cat: CubeCat,
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a),
cube-context-adjoin: X.A,
psc-adjoin: X.A,
cube-set-restriction: f(s),
psc-restriction: f(s),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f),
cc-adjoin-cube: (v;u),
psc-adjoin-set: (v;u)
Lemmas referenced :
psc-adjoin-set_wf,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cat_ob_pair_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesis,
sqequalRule,
isectElimination,
Error :memTop
Latex:
\mforall{}X:j\mvdash{}. \mforall{}A:\{X \mvdash{} \_\}. \mforall{}J:fset(\mBbbN{}). \mforall{}v:X(J). \mforall{}u:A(v). ((v;u) \mmember{} X.A(J))
Date html generated:
2020_05_20-PM-01_54_36
Last ObjectModification:
2020_04_03-PM-08_29_10
Theory : cubical!type!theory
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