Nuprl Lemma : csm-ap-type-fst-adjoin
∀[X:j⊢]. ∀[B:{X ⊢ _}]. ∀[s,u:Top]. (((B)p)(s;u) ~ (B)s)
Proof
Definitions occuring in Statement :
csm-adjoin: (s;u),
cc-fst: p,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
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,
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
cc-fst: p,
psc-fst: p,
csm-adjoin: (s;u),
pscm-adjoin: (s;u)
Lemmas referenced :
pscm-ap-type-fst-adjoin,
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{}[B:\{X \mvdash{} \_\}]. \mforall{}[s,u:Top]. (((B)p)(s;u) \msim{} (B)s)
Date html generated:
2020_05_20-PM-01_57_27
Last ObjectModification:
2020_04_03-PM-08_31_30
Theory : cubical!type!theory
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