Nuprl Lemma : csm-ap-type-fst-id-adjoin
∀[X:j⊢]. ∀[B:{X ⊢ _}]. ∀[u:Top]. (((B)p)[u] = B ∈ {X ⊢ _})
Proof
Definitions occuring in Statement :
csm-id-adjoin: [u],
cc-fst: p,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ 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-id-adjoin: [u],
pscm-id-adjoin: [u],
csm-adjoin: (s;u),
pscm-adjoin: (s;u),
csm-id: 1(X),
pscm-id: 1(X)
Lemmas referenced :
pscm-ap-type-fst-id-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{}[u:Top]. (((B)p)[u] = B)
Date html generated:
2020_05_20-PM-01_57_36
Last ObjectModification:
2020_04_03-PM-08_31_37
Theory : cubical!type!theory
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