Nuprl Lemma : groupoid-cat_wf
∀[G:Groupoid]. (cat(G) ∈ SmallCategory)
Proof
Definitions occuring in Statement :
groupoid-cat: cat(G)
,
groupoid: Groupoid
,
small-category: SmallCategory
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
Definitions unfolded in proof :
pi1: fst(t)
,
groupoid: Groupoid
,
groupoid-cat: cat(G)
,
member: t ∈ T
,
uall: ∀[x:A]. B[x]
Lemmas referenced :
groupoid_wf
Rules used in proof :
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
thin,
productElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[G:Groupoid]. (cat(G) \mmember{} SmallCategory)
Date html generated:
2016_05_18-AM-11_54_21
Last ObjectModification:
2015_12_28-PM-02_23_07
Theory : small!categories
Home
Index