Nuprl Lemma : presheaf-it_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. (* ∈ {X ⊢ _:1})
Proof
Definitions occuring in Statement :
presheaf-it: *,
presheaf-unit: 1,
presheaf-term: {X ⊢ _:A},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
presheaf-unit: 1,
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf-it: *,
subtype_rel: A ⊆r B
Lemmas referenced :
discrete-presheaf-term_wf,
unit_wf2,
it_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
instantiate,
applyEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. (* \mmember{} \{X \mvdash{} \_:1\})
Date html generated:
2020_05_20-PM-01_34_44
Last ObjectModification:
2020_04_02-PM-06_33_56
Theory : presheaf!models!of!type!theory
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