Nuprl Lemma : bag-member_wf
∀[T:Type]. ∀[x:T]. ∀[bs:bag(T)]. (x ↓∈ bs ∈ ℙ)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag: bag(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-member: x ↓∈ bs,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
squash_wf,
exists_wf,
list_wf,
equal_wf,
bag_wf,
list-subtype-bag,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
productEquality,
applyEquality,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[bs:bag(T)]. (x \mdownarrow{}\mmember{} bs \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-06_24_48
Last ObjectModification:
2018_03_23-PM-01_22_22
Theory : bags
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