Nuprl Lemma : csm-adjoin-wf
∀[Gamma,Delta:j⊢]. ∀[A:{Gamma ⊢' _}]. ∀[sigma:Delta j⟶ Gamma]. ∀[u:{Delta ⊢ _:(A)sigma}].
((sigma;u) ∈ Delta ij⟶ Gamma.A)
Proof
Definitions occuring in Statement :
csm-adjoin: (s;u),
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
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),
cube-set-restriction: f(s),
psc-restriction: f(s),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f),
csm-adjoin: (s;u),
pscm-adjoin: (s;u)
Lemmas referenced :
pscm-adjoin-wf,
cube-cat_wf,
cubical-type-sq-presheaf-type,
cubical-term-sq-presheaf-term
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
instantiate,
Error :memTop
Latex:
\mforall{}[Gamma,Delta:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{}' \_\}]. \mforall{}[sigma:Delta j{}\mrightarrow{} Gamma]. \mforall{}[u:\{Delta \mvdash{} \_:(A)sigma\}].
((sigma;u) \mmember{} Delta ij{}\mrightarrow{} Gamma.A)
Date html generated:
2020_05_20-PM-01_56_13
Last ObjectModification:
2020_04_04-AM-09_36_44
Theory : cubical!type!theory
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