{ 
[A,B:Type]. [base:B]. [f:B 
A B]. [size:
]. [num:A ].
[P:A 
].
(collect_filter_accum_fun(b,v.f[b;v];base;size;v.num[v];v.P[v])
{s:
B ( + Top)| (
isl(snd(snd(snd(s))))) 
(1 
(fst(s)))}
A
{s: B ( + Top)|
(isl(snd(snd(snd(s))))) (1 (fst(s)))} ) }
{ Proof }
Definitions occuring in Statement :
collect_filter_accum_fun: collect_filter_accum_fun(b,v.f[b; v];base;size;v.num[v];v.P[v]),
isl: isl(x),
assert: b,
bool: ,
nat_plus: ,
nat: ,
uall: [x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
le: A B,
implies: P Q,
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
product: x:A B[x],
union: left + right,
natural_number: $n,
int: ,
universe: Type
Definitions :
uall: [x:A]. B[x],
nat: ,
member: t T,
top: Top,
implies: P Q,
assert: b,
isl: isl(x),
pi2: snd(t),
le: A B,
pi1: fst(t),
collect_filter_accum_fun: collect_filter_accum_fun(b,v.f[b; v];base;size;v.num[v];v.P[v]),
so_apply: x[s1;s2],
so_apply: x[s],
spreadn: spread4,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
has-value: has-value(a),
all: x:A. B[x],
prop: 
,
false: False,
so_lambda: 
x.t[x],
subtype: S 
T,
not: 
A,
nat_plus: ,
bool: ,
unit: Unit,
iff: P 
Q,
and: P 
Q,
uimplies: b supposing a,
it: 
Lemmas :
rational-has-value,
int-rational,
nat_wf,
bool_wf,
lt_int_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
false_wf,
isl_wf,
pi2_wf,
le_wf,
pi1_wf_top,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
assert_of_eq_int,
true_wf,
not_wf,
assert_of_bnot,
not_functionality_wrt_uiff,
nat_properties,
int_inc,
eq_int_wf,
btrue_wf,
bfalse_wf,
top_wf,
nat_plus_wf
\mforall{}[A,B:Type]. \mforall{}[base:B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B]. \mforall{}[size:\mBbbN{}\msupplus{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}].
(collect\_filter\_accum\_fun(b,v.f[b;v];base;size;v.num[v];v.P[v]) \mmember{} \{s:\mBbbZ{} \mtimes{} \mBbbN{} \mtimes{} B \mtimes{} (\mBbbB{} + Top)|
(\muparrow{}isl(snd(snd(snd(s)))))
{}\mRightarrow{} (1 \mleq{} (fst(s)))\}
{}\mrightarrow{} A
{}\mrightarrow{} \{s:\mBbbZ{} \mtimes{} \mBbbN{} \mtimes{} B \mtimes{} (\mBbbB{} + Top)|
(\muparrow{}isl(snd(snd(snd(s)))))
{}\mRightarrow{} (1 \mleq{} (fst(s)))\} )
Date html generated:
2011_08_16-AM-11_05_01
Last ObjectModification:
2011_06_18-AM-09_37_38
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