Nuprl Lemma : singleton_properties
∀[T:Type]. ∀[a:T]. ∀[x:{a:T}]. (x = a ∈ T)
Proof
Definitions occuring in Statement :
singleton: {a:T},
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
singleton: {a:T}
Lemmas referenced :
singleton_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[x:\{a:T\}]. (x = a)
Date html generated:
2016_05_13-PM-03_15_20
Last ObjectModification:
2016_01_06-PM-05_21_57
Theory : core_2
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