Nuprl Lemma : cat-ob_wf
∀[C:SmallCategory]. (cat-ob(C) ∈ Type)
Proof
Definitions occuring in Statement :
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
spreadn: spread4,
pi1: fst(t),
small-category: SmallCategory,
cat-ob: cat-ob(C),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf
Rules used in proof :
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
cumulativity,
productElimination,
rename,
thin,
setElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C:SmallCategory]. (cat-ob(C) \mmember{} Type)
Date html generated:
2020_05_20-AM-07_49_27
Last ObjectModification:
2015_12_28-PM-02_24_11
Theory : small!categories
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