Nuprl Lemma : bag-no-repeats-implies-disjoint
∀[T:Type]. ∀[as,bs:bag(T)]. bag-disjoint(T;as;bs) supposing bag-no-repeats(T;as + bs)
Proof
Definitions occuring in Statement :
bag-disjoint: bag-disjoint(T;as;bs),
bag-no-repeats: bag-no-repeats(T;bs),
bag-append: as + bs,
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bag-disjoint: bag-disjoint(T;as;bs),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
uiff: uiff(P;Q),
prop: ℙ,
guard: {T}
Lemmas referenced :
bag-append-no-repeats,
and_wf,
bag-member_wf,
bag-no-repeats_wf,
bag-append_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
productElimination,
lemma_by_obid,
isectElimination,
because_Cache,
hypothesisEquality,
hypothesis,
independent_pairFormation,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:bag(T)]. bag-disjoint(T;as;bs) supposing bag-no-repeats(T;as + bs)
Date html generated:
2016_05_15-PM-02_51_52
Last ObjectModification:
2015_12_27-AM-09_33_00
Theory : bags
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