Nuprl Lemma : fset-disjoint_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:fset(T)]. (fset-disjoint(eq;as;bs) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fset-disjoint: fset-disjoint(eq;as;bs),
fset: fset(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-disjoint: fset-disjoint(eq;as;bs)
Lemmas referenced :
fset-null_wf,
fset-intersection_wf,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:fset(T)]. (fset-disjoint(eq;as;bs) \mmember{} \mBbbB{})
Date html generated:
2017_02_20-AM-10_49_16
Last ObjectModification:
2017_02_03-AM-10_53_14
Theory : finite!sets
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