Nuprl Lemma : s-filter_wf
∀[T:Type]. ∀[as:T List]. ∀[P:{a:T| (a ∈ as)} ⟶ 𝔹]. s-filter(P;as) ∈ T List supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
s-filter: s-filter(p;as),
l_member: (x ∈ l),
list: T List,
bool: 𝔹,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
s-filter: s-filter(p;as),
prop: ℙ
Lemmas referenced :
list-subtype,
reduce_wf,
l_member_wf,
list_wf,
ifthenelse_wf,
s-insert_wf,
nil_wf,
subtype_rel_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setEquality,
hypothesis,
lambdaEquality,
applyEquality,
independent_isectElimination,
setElimination,
rename,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as:T List]. \mforall{}[P:\{a:T| (a \mmember{} as)\} {}\mrightarrow{} \mBbbB{}]. s-filter(P;as) \mmember{} T List supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2016_05_15-PM-03_52_15
Last ObjectModification:
2015_12_27-PM-01_23_23
Theory : general
Home
Index