Nuprl Lemma : presheaf_type_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. (presheaf_type{i:l}(C; X) ∈ 𝕌{[i'' | j']})
Proof
Definitions occuring in Statement :
presheaf_type: presheaf_type{i:l}(C; X),
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf_type: presheaf_type{i:l}(C; X),
subtype_rel: A ⊆r B
Lemmas referenced :
presheaf_wf1,
sets_wf,
small-category-cumulativity-2,
ps_context_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,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. (presheaf\_type\{i:l\}(C; X) \mmember{} \mBbbU{}\{[i'' | j']\})
Date html generated:
2020_05_20-PM-01_25_14
Last ObjectModification:
2020_04_01-AM-09_33_11
Theory : presheaf!models!of!type!theory
Home
Index