Nuprl Lemma : bag-count-member-no-repeats
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. ∀[x:T]. ((#x in bs) = 1 ∈ ℤ) supposing (bag-no-repeats(T;bs) and x ↓∈ bs)
Proof
Definitions occuring in Statement :
bag-count: (#x in bs),
bag-member: x ↓∈ bs,
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
prop: ℙ
Lemmas referenced :
bag-no-repeats-count,
bag-no-repeats_wf,
bag-member_wf,
bag_wf,
deq_wf,
bag-member-count
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
introduction,
independent_isectElimination,
independent_pairFormation,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. \mforall{}[x:T].
((\#x in bs) = 1) supposing (bag-no-repeats(T;bs) and x \mdownarrow{}\mmember{} bs)
Date html generated:
2016_05_15-PM-07_59_26
Last ObjectModification:
2015_12_27-PM-04_16_25
Theory : bags_2
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