Nuprl Lemma : bag-filter-is-sub-bag
∀[T:Type]. ∀p:T ⟶ 𝔹. ∀b:bag(T). sub-bag(T;[x∈b|p[x]];b)
Proof
Definitions occuring in Statement :
sub-bag: sub-bag(T;as;bs),
bag-filter: [x∈b|p[x]],
bag: bag(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
sub-bag: sub-bag(T;as;bs),
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
bag-filter-split,
bag-filter_wf,
bnot_wf,
subtype_rel_bag,
assert_wf,
equal_wf,
bag_wf,
bag-append_wf,
bool_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_pairFormation,
sqequalRule,
lambdaEquality,
applyEquality,
setEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}p:T {}\mrightarrow{} \mBbbB{}. \mforall{}b:bag(T). sub-bag(T;[x\mmember{}b|p[x]];b)
Date html generated:
2016_05_15-PM-02_45_17
Last ObjectModification:
2015_12_27-AM-09_37_38
Theory : bags
Home
Index