Nuprl Lemma : presheaf_wf1
∀[C:SmallCategory]. (presheaf{j:l}(C) ∈ 𝕌{[i | j']})
Proof
Definitions occuring in Statement :
presheaf: Presheaf(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf: Presheaf(C),
subtype_rel: A ⊆r B
Lemmas referenced :
cat-functor_wf,
op-cat_wf,
small-category-cumulativity-2,
type-cat_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[C:SmallCategory]. (presheaf\{j:l\}(C) \mmember{} \mBbbU{}\{[i | j']\})
Date html generated:
2020_05_20-AM-07_52_36
Last ObjectModification:
2020_04_01-AM-00_46_39
Theory : small!categories
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