Nuprl Lemma : csm-dependent_wf
∀X,Delta:j⊢. ∀A:{X ⊢ _}. ∀s:Delta j⟶ X. ((s)dep ∈ Delta.(A)s j⟶ X.A)
Proof
Definitions occuring in Statement :
csm-dependent: (s)dep,
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
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],
cube_set_map: A ⟶ B,
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),
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
cube-set-restriction: f(s),
psc-restriction: f(s),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f),
csm-dependent: (s)dep,
pscm-dependent: (s)dep,
csm-adjoin: (s;u),
pscm-adjoin: (s;u),
csm-comp: G o F,
pscm-comp: G o F,
typed-cc-fst: tp{i:l},
typed-psc-fst: tp{i:l},
cc-fst: p,
psc-fst: p,
typed-cc-snd: tq,
typed-psc-snd: tq,
cc-snd: q,
psc-snd: q
Lemmas referenced :
pscm-dependent_wf,
cube-cat_wf,
cubical-type-sq-presheaf-type
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesis,
sqequalRule,
isectElimination,
Error :memTop
Latex:
\mforall{}X,Delta:j\mvdash{}. \mforall{}A:\{X \mvdash{} \_\}. \mforall{}s:Delta j{}\mrightarrow{} X. ((s)dep \mmember{} Delta.(A)s j{}\mrightarrow{} X.A)
Date html generated:
2020_05_20-PM-02_00_34
Last ObjectModification:
2020_04_03-PM-08_33_35
Theory : cubical!type!theory
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