Nuprl Lemma : mapfilter-wf
∀[T,U:Type]. ∀[L:T List]. ∀[P:T ⟶ 𝔹]. ∀[f:{x:T| (x ∈ L) ∧ (↑P[x])}  ⟶ U].  (mapfilter(f;P;L) ∈ U List)
Proof
Definitions occuring in Statement : 
mapfilter: mapfilter(f;P;L)
, 
l_member: (x ∈ l)
, 
list: T List
, 
assert: ↑b
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
and: P ∧ Q
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
mapfilter: mapfilter(f;P;L)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_apply: x[s]
, 
and: P ∧ Q
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
Lemmas referenced : 
map_wf, 
and_wf, 
l_member_wf, 
assert_wf, 
filter_type, 
subtype_rel_dep_function, 
bool_wf, 
subtype_rel_self, 
set_wf, 
list-subtype, 
subtype_rel_list, 
list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
setEquality, 
hypothesisEquality, 
hypothesis, 
applyEquality, 
cumulativity, 
because_Cache, 
sqequalRule, 
lambdaEquality, 
independent_isectElimination, 
setElimination, 
rename, 
lambdaFormation, 
equalityTransitivity, 
equalitySymmetry, 
productEquality, 
dependent_set_memberEquality, 
independent_pairFormation, 
functionEquality, 
universeEquality, 
isect_memberFormation, 
introduction, 
axiomEquality, 
isect_memberEquality
Latex:
\mforall{}[T,U:Type].  \mforall{}[L:T  List].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[f:\{x:T|  (x  \mmember{}  L)  \mwedge{}  (\muparrow{}P[x])\}    {}\mrightarrow{}  U].
    (mapfilter(f;P;L)  \mmember{}  U  List)
Date html generated:
2016_05_14-PM-01_29_12
Last ObjectModification:
2015_12_26-PM-05_22_16
Theory : list_1
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