Nuprl Lemma : groupoid-map_wf
∀[G,H:Groupoid]. (groupoid-map(G;H) ∈ Type)
Proof
Definitions occuring in Statement :
groupoid-map: groupoid-map(G;H),
groupoid: Groupoid,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
groupoid-map: groupoid-map(G;H),
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
cat-functor_wf,
groupoid-cat_wf,
cat-ob_wf,
cat-arrow_wf,
equal_wf,
functor-ob_wf,
functor-arrow_wf,
groupoid-inv_wf,
groupoid_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
functionEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[G,H:Groupoid]. (groupoid-map(G;H) \mmember{} Type)
Date html generated:
2019_10_31-AM-07_24_52
Last ObjectModification:
2019_05_07-PM-06_01_58
Theory : small!categories
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