{ 
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [P,Q:A 
].
[f:x:A fp-> B[x]].
(filter(
pL.Q[fst(pL)];fpf-vals(eq;P;f))
~ fpf-vals(eq;a.((P a) 
(Q a));f)) }
{ Proof }
Definitions occuring in Statement :
fpf-vals: fpf-vals(eq;P;f),
fpf: a:A fp-> B[a],
band: p q,
bool: ,
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
apply: f a,
lambda: x.A[x],
function: x:A B[x],
universe: Type,
sqequal: s ~ t,
filter: filter(P;l),
deq: EqDecider(T)
Definitions :
so_lambda: 
x.t[x],
so_apply: x[s],
member: t 
T,
pi2: snd(t),
let: let,
fpf-vals: fpf-vals(eq;P;f),
pi1: fst(t),
ycomb: Y,
reduce: reduce(f;k;as),
zip: zip(as;bs),
filter: filter(P;l),
bfalse: ff,
prop: 
,
btrue: tt,
implies: P 
Q,
all: x:A. B[x],
ifthenelse: if b then t else f fi ,
band: p q,
map: map(f;as),
uall: [x:A]. B[x],
fpf: a:A fp-> B[a],
and: P Q,
iff: P 
Q,
unit: Unit,
bool: ,
it: 
Lemmas :
deq_wf,
bool_wf,
fpf_wf,
assert_of_bnot,
eqff_to_assert,
bnot_wf,
uiff_transitivity,
not_wf,
eqtt_to_assert,
assert_wf,
iff_weakening_uiff
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[P,Q:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:x:A fp-> B[x]].
(filter(\mlambda{}pL.Q[fst(pL)];fpf-vals(eq;P;f)) \msim{} fpf-vals(eq;\mlambda{}a.((P a) \mwedge{}\msubb{} (Q a));f))
Date html generated:
2011_08_10-AM-08_03_40
Last ObjectModification:
2011_06_18-AM-08_22_14
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