{ collectfilterfun2() 
{s:
( + Top)|
(
isl(snd(snd(s)))) 
(1 
(fst(s)))} 
( + Top) }
{ Proof }
Definitions occuring in Statement :
collectfilterfun2: collectfilterfun2(),
isl: isl(x),
assert: b,
bool: ,
nat: ,
top: Top,
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:
Definitions :
void: Void,
member: t T,
isect: 
x:A. B[x],
top: Top,
product: x:A B[x],
assert: b,
nat: ,
bool: ,
union: left + right,
function: x:A B[x],
all: 
x:A. B[x],
subtype: S 
T,
spreadn: spread3,
eclass: EClass(A[eo; e]),
equal: s = t,
subtype_rel: A r B,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
set: {x:A| B[x]} ,
implies: P Q,
universe: Type,
prop: 
,
int: ,
pi1: fst(t),
natural_number: $n,
le: A B,
lambda: 
x.A[x],
so_lambda: 
x.t[x],
pi2: snd(t),
isl: isl(x),
collectfilterfun2: collectfilterfun2(),
inr: inr x ,
pair: <a, b>,
false: False,
not: 
A,
inl: inl x ,
it: 
,
bfalse: ff,
es-E-interface: E(X),
unit: Unit,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
subtract: n - m,
sum-map: 
f[x] for x L,
sum: (f[x] | x < k),
imax: imax(a;b),
or: P 
Q,
multiply: n * m,
guard: {T},
minus: -n,
add: n + m,
less_than: a < b,
rationals: 
,
real: 
,
length: ||as||,
l_member: (x l),
apply: f a,
so_apply: x[s],
eq_knd: a = b,
fpf-dom: x dom(f),
in-eclass: e 
X,
bnot: b,
btrue: tt,
limited-type: LimitedType,
and: P 
Q,
iff: P 
Q,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: Error :set_blt,
infix_ap: x f y,
grp_blt: Error :grp_blt,
b-exists: (
i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
q_le: q_le(r;s),
q_less: q_less(a;b),
qeq: qeq(r;s),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
eq_str: eq_str(x;y),
bimplies: p q,
band: p q,
bor: p q,
sq_type: SQType(T),
spread: spread def,
true: True
Lemmas :
ifthenelse_wf,
eqtt_to_assert,
iff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
not_wf,
bfalse_wf,
subtype_rel_wf,
assert_wf,
isl_wf,
pi2_wf,
le_wf,
pi1_wf_top,
member_wf,
top_wf,
bool_wf,
nat_wf
collectfilterfun2() \mmember{} \{s:\mBbbZ{} \mtimes{} \mBbbN{} \mtimes{} \mBbbB{} \mtimes{} (\mBbbN{} \mtimes{} \mBbbB{} + Top)| (\muparrow{}isl(snd(snd(s)))) {}\mRightarrow{} (1 \mleq{} (fst(s)))\}
{}\mrightarrow{} (\mBbbN{} + Top)
Date html generated:
2010_08_27-PM-03_04_17
Last ObjectModification:
2010_03_26-PM-02_17_44
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