{ 
[A,B:Type]. [f:A 
bag(B)]. (MapFilterComb(A;B;f) 
CombinatorDef) }
{ Proof }
Definitions occuring in Statement :
MapFilterComb: MapFilterComb(A;B;f),
combinator-def: CombinatorDef,
uall: [x:A]. B[x],
member: t T,
function: x:A B[x],
universe: Type,
bag: bag(T)
Definitions :
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
void: Void,
fpf-sub: f 
g,
squash: 
T,
sq_stable: SqStable(P),
top: Top,
true: True,
fpf-cap: f(x)?z,
filter: filter(P;l),
IdLnk: IdLnk,
Id: Id,
rationals: 
,
append: as @ bs,
locl: locl(a),
Knd: Knd,
false: False,
lt_int: i <z j,
le_int: i 
z j,
limited-type: LimitedType,
bfalse: ff,
btrue: tt,
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p 
q,
band: p 
q,
bor: p 
q,
bnot: 
b,
unit: Unit,
bool: 
,
so_apply: x[s],
implies: P Q,
union: left + right,
or: P Q,
guard: {T},
l_member: (x l),
assert: 
b,
es-E-interface: E(X),
sq_type: SQType(T),
permutation: permutation(T;L1;L2),
list: type List,
real: 
,
grp_car: |g|,
int: 
,
quotient: x,y:A//B[x; y],
subtype: S T,
suptype: suptype(S; T),
eclass: EClass(A[eo; e]),
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: A,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
natural_number: $n,
apply: f a,
nat: 
,
ifthenelse: if b then t else f fi ,
empty-bag: {},
bag-only: only(bs),
eq_int: (i =
j),
bag-size: bag-size(bs),
prop: 
,
subtype_rel: A r B,
set: {x:A| B[x]} ,
lambda: 
x.A[x],
so_lambda: 
x.t[x],
SimpleComb1: SimpleComb1(T1.P1[T1];T.F[T];a.H[a]),
all: x:A. B[x],
bag: bag(T),
combinator-def: CombinatorDef,
MapFilterComb: MapFilterComb(A;B;f),
function: x:A B[x],
axiom: Ax,
universe: Type,
isect: 
x:A. B[x],
member: t T,
equal: s = t,
uall: [x:A]. B[x]
Lemmas :
bag_wf,
member_wf,
subtype_rel_wf,
SimpleComb1_wf,
ifthenelse_wf,
eq_int_wf,
bag-size_wf,
nat_wf,
bag-only_wf,
empty-bag_wf,
permutation_wf,
subtype_base_sq,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
assert_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
bnot_wf,
subtype_rel_bag,
sq_stable__subtype_rel
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. (MapFilterComb(A;B;f) \mmember{} CombinatorDef)
Date html generated:
2011_08_17-PM-06_27_28
Last ObjectModification:
2011_06_18-AM-11_50_12
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