Nuprl Lemma : mapfilter_wf
∀[T:Type]. ∀[L:T List]. ∀[P:T ⟶ 𝔹]. ∀[T':Type]. ∀[f:{x:T| ↑(P x)} ⟶ T']. (mapfilter(f;P;L) ∈ T' List)
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
list: T List,
assert: ↑b,
bool: 𝔹,
uall: ∀[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,
mapfilter: mapfilter(f;P;L),
prop: ℙ
Lemmas referenced :
filter_type,
map_wf,
assert_wf,
bool_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setEquality,
applyEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :setIsType,
Error :universeIsType,
isect_memberEquality,
functionEquality,
Error :inhabitedIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[T':Type]. \mforall{}[f:\{x:T| \muparrow{}(P x)\} {}\mrightarrow{} T'].
(mapfilter(f;P;L) \mmember{} T' List)
Date html generated:
2019_06_20-PM-01_24_59
Last ObjectModification:
2018_09_26-PM-05_28_58
Theory : list_1
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