Nuprl Lemma : mapfilter-bor
∀T,U:Type. ∀f:T ─→ U. ∀P,Q:T ─→ 𝔹. ∀L:T List.
sub-bag(U;mapfilter(f;λx.(P[x] ∨bQ[x]);L);mapfilter(f;P;L) @ mapfilter(f;Q;L))
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
append: as @ bs,
list: T List,
bor: p ∨bq,
bool: 𝔹,
so_apply: x[s],
all: ∀x:A. B[x],
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type,
sub-bag: sub-bag(T;as;bs)
Lemmas :
mapfilter_wf,
bool_wf,
eqtt_to_assert,
subtype_rel_dep_function,
assert_wf,
set_wf,
list-subtype-bag,
mapfilter-bor-eq,
equal_wf,
bag_wf,
append_wf,
bag-append_wf,
bor_wf,
list_wf
Latex:
\mforall{}T,U:Type. \mforall{}f:T {}\mrightarrow{} U. \mforall{}P,Q:T {}\mrightarrow{} \mBbbB{}. \mforall{}L:T List.
sub-bag(U;mapfilter(f;\mlambda{}x.(P[x] \mvee{}\msubb{}Q[x]);L);mapfilter(f;P;L) @ mapfilter(f;Q;L))
Date html generated:
2015_07_21-PM-04_52_41
Last ObjectModification:
2015_01_28-AM-08_43_15
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