Nuprl Lemma : bag-filter-wf3
∀[T:Type]. ∀[p:T ⟶ 𝔹]. ∀[bs:bag(T)]. ([x∈bs|p[x]] ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-filter: [x∈b|p[x]],
bag: bag(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
bag-filter_wf,
subtype_rel_bag,
assert_wf,
bag_wf,
bool_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
setEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[p:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[bs:bag(T)]. ([x\mmember{}bs|p[x]] \mmember{} bag(T))
Date html generated:
2016_05_15-PM-02_23_00
Last ObjectModification:
2015_12_27-AM-09_54_25
Theory : bags
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