Nuprl Lemma : bag-member-evidence
∀[T:Type]. ∀[b:bag(T)]. ∀[x:T]. Ax ∈ x ↓∈ b supposing x ↓∈ b
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ
Lemmas referenced :
bag_wf,
bag-member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
imageElimination,
hypothesis,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. \mforall{}[x:T]. Ax \mmember{} x \mdownarrow{}\mmember{} b supposing x \mdownarrow{}\mmember{} b
Date html generated:
2016_05_15-PM-02_39_40
Last ObjectModification:
2016_01_16-AM-08_48_06
Theory : bags
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