Nuprl Lemma : cubical-app-id-fun
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[u:{X ⊢ _:A}]. (app(cubical-id-fun(X); u) = u ∈ {X ⊢ _:A})
Proof
Definitions occuring in Statement :
cubical-app: app(w; u),
cubical-id-fun: cubical-id-fun(X),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cubical-app: app(w; u),
presheaf-app: app(w; u),
cubical-id-fun: cubical-id-fun(X),
presheaf-id-fun: presheaf-id-fun(X),
cubical-lam: cubical-lam(X;b),
presheaf-lam: presheaf-lam(X;b),
cubical-lambda: (λb),
presheaf-lambda: (λb),
cc-snd: q,
psc-snd: q,
cc-adjoin-cube: (v;u),
psc-adjoin-set: (v;u),
cube-set-restriction: f(s),
psc-restriction: f(s),
cube-cat: CubeCat,
all: ∀x:A. B[x]
Lemmas referenced :
presheaf-app-id-fun,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cubical-term-sq-presheaf-term,
cat_id_tuple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop,
dependent_functionElimination
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u:\{X \mvdash{} \_:A\}]. (app(cubical-id-fun(X); u) = u)
Date html generated:
2020_05_20-PM-02_30_54
Last ObjectModification:
2020_04_03-PM-08_41_11
Theory : cubical!type!theory
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