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:
2020_05_20-AM-07_55_09
Last ObjectModification:
2015_12_28-PM-02_23_07
Theory : small!categories
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