Nuprl Lemma : csm-ap-id-term
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[t:{Gamma ⊢ _:A}]. ((t)1(Gamma) = t ∈ {Gamma ⊢ _:A})
Proof
Definitions occuring in Statement :
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
csm-id: 1(X),
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
csm-ap-term: (t)s,
pscm-ap-term: (t)s,
csm-ap: (s)x,
pscm-ap: (s)x,
csm-id: 1(X),
pscm-id: 1(X)
Lemmas referenced :
pscm-ap-id-term,
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:\{Gamma \mvdash{} \_\}]. \mforall{}[t:\{Gamma \mvdash{} \_:A\}]. ((t)1(Gamma) = t)
Date html generated:
2020_05_20-PM-01_53_43
Last ObjectModification:
2020_04_03-PM-08_28_27
Theory : cubical!type!theory
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