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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