Nuprl Lemma : typed-cc-snd_wf
∀G:j⊢. ∀A:{G ⊢ _}. (tq ∈ {G.A ⊢ _:(A)tp{i:l}})
Proof
Definitions occuring in Statement :
typed-cc-snd: tq,
typed-cc-fst: tp{i:l},
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
typed-cc-fst: tp{i:l},
typed-psc-fst: tp{i:l},
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),
typed-cc-snd: tq,
typed-psc-snd: tq,
cc-snd: q,
psc-snd: q
Lemmas referenced :
typed-psc-snd_wf,
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,
dependent_functionElimination,
thin,
hypothesis,
sqequalRule,
isectElimination,
Error :memTop
Latex:
\mforall{}G:j\mvdash{}. \mforall{}A:\{G \mvdash{} \_\}. (tq \mmember{} \{G.A \mvdash{} \_:(A)tp\{i:l\}\})
Date html generated:
2020_05_20-PM-01_55_28
Last ObjectModification:
2020_04_03-PM-08_29_54
Theory : cubical!type!theory
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