Nuprl Lemma : csm-ap-type-is-id
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[s:Gamma j⟶ Gamma]. (A)s = A ∈ {Gamma ⊢ _} supposing s = 1(Gamma) ∈ Gamma j⟶ Gamma
Proof
Definitions occuring in Statement :
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
csm-id: 1(X),
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
csm-id: 1(X),
pscm-id: 1(X),
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x
Lemmas referenced :
pscm-ap-type-is-id,
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{}[s:Gamma j{}\mrightarrow{} Gamma]. (A)s = A supposing s = 1(Gamma)
Date html generated:
2020_05_20-PM-01_49_48
Last ObjectModification:
2020_04_03-PM-08_27_12
Theory : cubical!type!theory
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