Nuprl Lemma : cubical-fst-pair
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[u:{X ⊢ _:A}]. ∀[v:Top]. (cubical-pair(u;v).1 = u ∈ {X ⊢ _:A})
Proof
Definitions occuring in Statement :
cubical-pair: cubical-pair(u;v),
cubical-fst: p.1,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cubical-fst: p.1,
presheaf-fst: p.1,
cubical-pair: cubical-pair(u;v),
presheaf-pair: presheaf-pair(u;v)
Lemmas referenced :
presheaf-fst-pair,
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{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[u:\{X \mvdash{} \_:A\}]. \mforall{}[v:Top]. (cubical-pair(u;v).1 = u)
Date html generated:
2020_05_20-PM-02_29_59
Last ObjectModification:
2020_04_03-PM-08_40_18
Theory : cubical!type!theory
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