Nuprl Lemma : csm-ap-term-p
∀[Gamma:j⊢]. ∀[A,T:{Gamma ⊢ _}]. ∀[t:{Gamma ⊢ _:A}]. ((t)p ∈ {Gamma.T ⊢ _:(A)p})
Proof
Definitions occuring in Statement :
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
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,
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
cc-fst: p,
psc-fst: p,
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-ap-term: (t)s,
pscm-ap-term: (t)s
Lemmas referenced :
pscm-ap-term-p,
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:j\mvdash{}]. \mforall{}[A,T:\{Gamma \mvdash{} \_\}]. \mforall{}[t:\{Gamma \mvdash{} \_:A\}]. ((t)p \mmember{} \{Gamma.T \mvdash{} \_:(A)p\})
Date html generated:
2020_05_20-PM-01_56_04
Last ObjectModification:
2020_04_03-PM-08_30_33
Theory : cubical!type!theory
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