Nuprl Lemma : groupoid_wf
Groupoid ∈ 𝕌'
Proof
Definitions occuring in Statement :
groupoid: Groupoid,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
groupoid: Groupoid,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
small-category_wf,
cat-ob_wf,
cat-arrow_wf,
all_wf,
equal_wf,
cat-comp_wf,
cat-id_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
productEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
setEquality,
functionEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
cumulativity,
universeEquality,
because_Cache,
functionExtensionality
Latex:
Groupoid \mmember{} \mBbbU{}'
Date html generated:
2020_05_20-AM-07_55_04
Last ObjectModification:
2017_07_28-AM-09_20_07
Theory : small!categories
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