Nuprl Lemma : fset-singleton_wf
∀[T:Type]. ∀[x:T]. ({x} ∈ fset(T))
Proof
Definitions occuring in Statement :
fset-singleton: {x},
fset: fset(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
fset-singleton: {x},
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
cons_wf,
nil_wf,
list_subtype_fset
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. (\{x\} \mmember{} fset(T))
Date html generated:
2016_05_14-PM-03_38_47
Last ObjectModification:
2015_12_26-PM-06_41_56
Theory : finite!sets
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