Nuprl Lemma : ps-context-map-ap-type
∀[C:SmallCategory]. ∀[I:cat-ob(C)]. ∀[Gamma:ps_context{j:l}(C)]. ∀[rho:Gamma(I)]. ∀[A:{Gamma ⊢ _}].
  ((A)<rho> ∈ Yoneda(I) ⊢ )
Proof
Definitions occuring in Statement : 
pscm-ap-type: (AF)s
, 
presheaf-type: {X ⊢ _}
, 
ps-context-map: <rho>
, 
Yoneda: Yoneda(I)
, 
I_set: A(I)
, 
ps_context: __⊢
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
cat-ob: cat-ob(C)
, 
small-category: SmallCategory
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
all: ∀x:A. B[x]
Lemmas referenced : 
pscm-ap-type_wf, 
ps_context_cumulativity2, 
small-category-cumulativity-2, 
Yoneda_wf, 
ps-context-map_wf, 
presheaf-type_wf, 
I_set_wf, 
ps_context_wf, 
cat-ob_wf, 
small-category_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
thin, 
instantiate, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
applyEquality, 
hypothesis, 
sqequalRule, 
dependent_functionElimination, 
because_Cache, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeIsType, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory].  \mforall{}[I:cat-ob(C)].  \mforall{}[Gamma:ps\_context\{j:l\}(C)].  \mforall{}[rho:Gamma(I)].  \mforall{}[A:\{Gamma  \mvdash{}  \_\}].
    ((A)<rho>  \mmember{}  Yoneda(I)  \mvdash{}  )
Date html generated:
2020_05_20-PM-01_26_17
Last ObjectModification:
2020_04_01-AM-11_51_00
Theory : presheaf!models!of!type!theory
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