Nuprl Lemma : filter_wf
∀[T:Type]. ∀[l:T List]. ∀[P:T ⟶ 𝔹]. (filter(P;l) ∈ T List)
Proof
Definitions occuring in Statement :
filter: filter(P;l),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
filter: filter(P;l)
Lemmas referenced :
reduce_wf,
list_wf,
ifthenelse_wf,
cons_wf,
nil_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :universeIsType,
isect_memberEquality,
functionEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. (filter(P;l) \mmember{} T List)
Date html generated:
2019_06_20-PM-00_39_13
Last ObjectModification:
2018_09_26-PM-02_05_47
Theory : list_0
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