{ 
[A,B:Type]. [b1,b2:bag(dataflow(A;bag(B)))].
(dataflow-bags-equiv(A;B;b1;b2)
{m:A
dataflow-bags-equiv(A;B;bag-map(
x.(fst(x(m)));
b1);bag-map(x.(fst(x(m)));b2))}) }
{ Proof }
Definitions occuring in Statement :
dataflow-bags-equiv: dataflow-bags-equiv(A;B;b1;b2),
dataflow-ap: df(a),
dataflow: dataflow(A;B),
uall: [x:A]. B[x],
guard: {T},
pi1: fst(t),
all: x:A. B[x],
implies: P Q,
lambda: x.A[x],
universe: Type,
bag-map: bag-map(f;bs),
bag: bag(T)
Definitions :
length: ||as||,
add: n + m,
true: True,
map: map(f;as),
subtype: S 
T,
sqequal: s ~ t,
primrec: primrec(n;b;c),
nat: 
,
top: Top,
corec: corec(T.F[T]),
l_member: (x 
l),
void: Void,
false: False,
list: type List,
so_lambda: 
x.t[x],
pair: <a, b>,
fpf: a:A fp-> B[a],
set: {x:A| B[x]} ,
quotient: x,y:A//B[x; y],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
prop: 
,
axiom: Ax,
last: last(L),
dataflow-ap: df(a),
pi1: fst(t),
bag-map: bag-map(f;bs),
bag-combine: 
xbs.f[x],
listp: A List
,
guard: {T},
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
implies: P Q,
dataflow-bags-equiv: dataflow-bags-equiv(A;B;b1;b2),
function: x:A 
B[x],
member: t T,
lambda: x.A[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
MaAuto: Error :MaAuto,
data-stream: data-stream(P;L),
null: null(as),
assert: 
b,
not: 
A,
bag: bag(T),
dataflow: dataflow(A;B),
all: x:A. B[x],
AssertBY: Error :AssertBY,
Unfold: Error :Unfold,
tactic: Error :tactic,
isect2: T1 T2,
b-union: A B,
sq_type: SQType(T),
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
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,
bimplies: p q,
band: p q,
bor: p 
q,
bnot: b,
int: 
,
unit: Unit,
ifthenelse: if b then t else f fi ,
squash: 
T,
tl: tl(l),
hd: hd(l),
rev_implies: P 
Q,
iff: P Q,
fpf-sub: f g,
deq: EqDecider(T),
ma-state: State(ds),
permutation: permutation(T;L1;L2),
nil: [],
fpf-cap: f(x)?z,
bool: 
,
intensional-universe: IType,
sq_stable: SqStable(P),
apply: f a,
so_apply: x[s],
union: left + right,
or: P Q,
eq_knd: a = b,
fpf-dom: x dom(f),
pi2: snd(t),
limited-type: LimitedType,
base: Base,
ndlist: ndlist(T),
THENM: Error :THENM,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try,
cons: [car / cdr]
Lemmas :
data-stream-cons,
cons_wf_listp,
intensional-universe_wf,
null_wf,
permutation_wf,
subtype_rel_list,
bag-combine-map,
iff_wf,
rev_implies_wf,
last_wf,
pi1_wf_top,
bag-combine_wf,
pi2_wf,
squash_wf,
last-cons,
ifthenelse_wf,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_null,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
bnot_wf,
subtype_base_sq,
list_subtype_base,
nat_wf,
length_wf_nat,
dataflow_subtype,
subtype_rel_self,
dataflow_wf,
bag_wf,
pi1_wf,
dataflow-ap_wf,
bag-map_wf,
listp_wf,
dataflow-bags-equiv_wf,
assert_wf,
not_wf,
false_wf,
data-stream_wf,
pos_length2,
null_wf3,
top_wf,
member_wf,
subtype_rel_wf,
null-data-stream,
listp_properties,
true_wf
\mforall{}[A,B:Type]. \mforall{}[b1,b2:bag(dataflow(A;bag(B)))].
(dataflow-bags-equiv(A;B;b1;b2)
{}\mRightarrow{} \{\mforall{}m:A. dataflow-bags-equiv(A;B;bag-map(\mlambda{}x.(fst(x(m)));b1);bag-map(\mlambda{}x.(fst(x(m)));b2))\})
Date html generated:
2011_08_16-AM-09_49_00
Last ObjectModification:
2011_04_27-PM-04_17_31
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