Nuprl Lemma : cc-fstfst_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[B:{Gamma.A ⊢ _}]. (pp ∈ Gamma.A.B ij⟶ Gamma)
Proof
Definitions occuring in Statement :
cc-fstfst: pp,
cube-context-adjoin: X.A,
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-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),
cube_set_map: A ⟶ B,
cc-fstfst: pp,
psc-fstfst: pp
Lemmas referenced :
psc-fstfst_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:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[B:\{Gamma.A \mvdash{} \_\}]. (pp \mmember{} Gamma.A.B ij{}\mrightarrow{} Gamma)
Date html generated:
2020_05_20-PM-01_55_10
Last ObjectModification:
2020_04_04-AM-09_29_35
Theory : cubical!type!theory
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