Nuprl Lemma : squash-bag-member
∀[T:Type]. ∀[x:T]. ∀[bs:bag(T)]. uiff(↓x ↓∈ bs;x ↓∈ bs)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag: bag(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
squash: ↓T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ
Lemmas referenced :
bag_wf,
bag-member_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
imageElimination,
hypothesis,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
lemma_by_obid,
isectElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[bs:bag(T)]. uiff(\mdownarrow{}x \mdownarrow{}\mmember{} bs;x \mdownarrow{}\mmember{} bs)
Date html generated:
2016_05_15-PM-02_36_32
Last ObjectModification:
2016_01_16-AM-08_51_05
Theory : bags
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