{ 
[A:Type]. [eq:EqDecider(A)]. [B:A 
Type]. [P:A 
].
[f:x:A fp-> B[x]].
(fpf-vals(eq;P;f) 
(x:{a:A| 
(P a)} 
B[x]) List) }
{ Proof }
Definitions occuring in Statement :
fpf-vals: fpf-vals(eq;P;f),
fpf: a:A fp-> B[a],
assert: b,
bool: ,
uall: [x:A]. B[x],
so_apply: x[s],
member: t T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x],
product: x:A B[x],
list: type List,
universe: Type,
deq: EqDecider(T)
Definitions :
so_lambda: 
x.t[x],
pi2: snd(t),
pi1: fst(t),
let: let,
fpf-vals: fpf-vals(eq;P;f),
member: t T,
so_apply: x[s],
uall: [x:A]. B[x],
bfalse: ff,
btrue: tt,
implies: P 
Q,
all: x:A. B[x],
ifthenelse: if b then t else f fi ,
prop: 
,
ycomb: Y,
reduce: reduce(f;k;as),
map: map(f;as),
filter: filter(P;l),
zip: zip(as;bs),
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,
uiff_transitivity,
eqtt_to_assert,
iff_weakening_uiff,
bnot_wf,
not_wf,
assert_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:x:A fp-> B[x]].
(fpf-vals(eq;P;f) \mmember{} (x:\{a:A| \muparrow{}(P a)\} \mtimes{} B[x]) List)
Date html generated:
2011_08_10-AM-08_03_18
Last ObjectModification:
2011_06_18-AM-08_21_01
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