Nuprl Lemma : bag-mapfilter_wf
∀[T,A:Type]. ∀P:T ⟶ 𝔹. ∀f:{x:T| ↑(P x)} ⟶ A. ∀bs:bag(T). (bag-mapfilter(f;P;bs) ∈ bag(A))
Proof
Definitions occuring in Statement :
bag-mapfilter: bag-mapfilter(f;P;bs),
bag: bag(T),
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
bag-mapfilter: bag-mapfilter(f;P;bs),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
bag-map_wf,
assert_wf,
bag-filter_wf,
bag_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setEquality,
applyEquality,
hypothesis,
lambdaEquality,
functionEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T,A:Type]. \mforall{}P:T {}\mrightarrow{} \mBbbB{}. \mforall{}f:\{x:T| \muparrow{}(P x)\} {}\mrightarrow{} A. \mforall{}bs:bag(T). (bag-mapfilter(f;P;bs) \mmember{} bag(A))
Date html generated:
2016_05_15-PM-02_23_46
Last ObjectModification:
2015_12_27-AM-09_53_56
Theory : bags
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