Nuprl Lemma : sq_stable__bag-member
∀[T:Type]. ∀[x:T]. ∀[bs:bag(T)]. SqStable(x ↓∈ bs)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag: bag(T),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-member: x ↓∈ bs,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ
Lemmas referenced :
bag-member_wf,
squash_wf,
l_member_wf,
list-subtype-bag,
bag_wf,
equal_wf,
and_wf,
list_wf,
exists_wf,
sq_stable__squash
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[bs:bag(T)]. SqStable(x \mdownarrow{}\mmember{} bs)
Date html generated:
2016_05_15-PM-02_36_35
Last ObjectModification:
2016_01_16-AM-08_50_42
Theory : bags
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