Nuprl Lemma : representable-psc_wf
∀[C:small-category{1:l}]. (representable-psc(C) ∈ 𝕌{3})
Proof
Definitions occuring in Statement :
representable-psc: representable-psc(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,
representable-psc: representable-psc(C),
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
small-category_wf,
ps_context_wf,
exists_wf,
cat-ob_wf,
equal_wf,
Yoneda_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
extract_by_obid,
setEquality,
thin,
isectElimination,
hypothesisEquality,
cumulativity,
lambdaEquality
Latex:
\mforall{}[C:small-category\{1:l\}]. (representable-psc(C) \mmember{} \mBbbU{}\{3\})
Date html generated:
2018_05_22-PM-09_59_34
Last ObjectModification:
2018_05_20-PM-09_42_35
Theory : presheaf!models!of!type!theory
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