Nuprl Lemma : cc-fst-csm-adjoin
∀[Gamma,Delta:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[sigma:Delta j⟶ Gamma]. ∀[u:{Delta ⊢ _:(A)sigma}].
(p o (sigma;u) = sigma ∈ Delta j⟶ Gamma)
Proof
Definitions occuring in Statement :
csm-adjoin: (s;u),
cc-fst: p,
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
csm-comp: G o F,
cube_set_map: A ⟶ B,
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,
cube_set_map: A ⟶ B,
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
csm-comp: G o F,
pscm-comp: G o F,
cc-fst: p,
psc-fst: p,
csm-adjoin: (s;u),
pscm-adjoin: (s;u)
Lemmas referenced :
psc-fst-pscm-adjoin,
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,
Error :memTop
Latex:
\mforall{}[Gamma,Delta:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[sigma:Delta j{}\mrightarrow{} Gamma]. \mforall{}[u:\{Delta \mvdash{} \_:(A)sigma\}].
(p o (sigma;u) = sigma)
Date html generated:
2020_05_20-PM-01_56_59
Last ObjectModification:
2020_04_03-PM-08_31_07
Theory : cubical!type!theory
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