Nuprl Lemma : csm-type-ap_wf
∀[Gamma,Delta:j⊢]. ∀[s:Delta j⟶ Gamma]. ∀[A:{Gamma ⊢ _}]. Delta ⊢ csm-type-ap(A;s)
Proof
Definitions occuring in Statement :
csm-type-ap: csm-type-ap(A;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-type-ap: csm-type-ap(A;s),
pscm-type-ap: pscm-type-ap(A;s),
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x
Lemmas referenced :
pscm-type-ap_wf,
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{}[Gamma,Delta:j\mvdash{}]. \mforall{}[s:Delta j{}\mrightarrow{} Gamma]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. Delta \mvdash{} csm-type-ap(A;s)
Date html generated:
2020_05_20-PM-01_49_24
Last ObjectModification:
2020_04_03-PM-08_26_54
Theory : cubical!type!theory
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