Nuprl Lemma : comma-slice-cat_wf
∀[A,C:SmallCategory]. ∀[S:Functor(A;C)]. ∀[x:cat-ob(C)]. ((S ↓ x) ∈ SmallCategory)
Proof
Definitions occuring in Statement :
comma-slice-cat: (S ↓ x),
cat-functor: Functor(C1;C2),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
comma-slice-cat: (S ↓ x)
Lemmas referenced :
comma-cat_wf,
unit-cat_wf,
const-functor_wf,
cat-ob_wf,
cat-functor_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,C:SmallCategory]. \mforall{}[S:Functor(A;C)]. \mforall{}[x:cat-ob(C)]. ((S \mdownarrow{} x) \mmember{} SmallCategory)
Date html generated:
2020_05_20-AM-07_56_38
Last ObjectModification:
2017_01_13-PM-04_49_15
Theory : small!categories
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