Nuprl Lemma : cc-adjoin-cube-restriction
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[J,K,g,v,u:Top]. (g((v;u)) ~ (g(v);(u v g)))
Proof
Definitions occuring in Statement :
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
cubical-type-ap-morph: (u a f),
cubical-type: {X ⊢ _},
cube-set-restriction: f(s),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube-set-restriction: f(s),
psc-restriction: f(s),
cube-context-adjoin: X.A,
psc-adjoin: X.A,
I_cube: A(I),
I_set: A(I),
cubical-type-at: A(a),
presheaf-type-at: A(a),
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-restriction,
cube-cat_wf,
cubical-type-sq-presheaf-type
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[J,K,g,v,u:Top]. (g((v;u)) \msim{} (g(v);(u v g)))
Date html generated:
2020_05_20-PM-01_54_44
Last ObjectModification:
2020_04_03-PM-08_29_18
Theory : cubical!type!theory
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