Nuprl Lemma : singleton_wf
∀[T:Type]. ∀[a:T]. ({a:T} ∈ Type)
Proof
Definitions occuring in Statement :
singleton: {a:T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
singleton: {a:T},
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. (\{a:T\} \mmember{} Type)
Date html generated:
2019_06_20-AM-11_18_04
Last ObjectModification:
2018_09_26-AM-10_25_11
Theory : core_2
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