{ 
[Info,A,B:Type]. [f:A 
bag(B)]. [es:EO+(Info)]. [X:EClass(A)]. [e:E].
(
(f[X])(e) ~ filter(
e.(bag-size(f X(e)) =
1);(X)(e))) }
{ Proof }
Definitions occuring in Statement :
es-interface-predecessors: (X)(e),
es-filter-image: f[X],
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
eq_int: (i = j),
uall: [x:A]. B[x],
apply: f a,
lambda: x.A[x],
function: x:A B[x],
natural_number: $n,
universe: Type,
sqequal: s ~ t,
filter: filter(P;l),
bag-size: bag-size(bs),
bag: bag(T)
Definitions :
es-prior-interface: prior(X),
es-interface-at: X@i,
tag-by: z
T,
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
intensional-universe: IType,
cond-class: [X?Y],
eq_knd: a = b,
rev_implies: P 
Q,
iff: P 
Q,
bfalse: ff,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (x
L.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
bor: p 
q,
bnot: 
b,
unit: Unit,
void: Void,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
fpf-dom: x dom(f),
false: False,
fpf-cap: f(x)?z,
permutation: permutation(T;L1;L2),
quotient: x,y:A//B[x; y],
atom_eq: atomeqn def,
rationals: 
,
locl: locl(a),
Knd: Knd,
atom: Atom$n,
squash: 
T,
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
valueall-type: valueall-type(T),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f 
g,
sq_stable: SqStable(P),
limited-type: LimitedType,
so_apply: x[s],
union: left + right,
or: P Q,
cons: [car / cdr],
exists: x:A. B[x],
suptype: suptype(S; T),
l_member: (x l),
nil: [],
qabs: |r|,
append: as @ bs,
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,
product: x:A B[x],
and: P 
Q,
uiff: uiff(P;Q),
base: Base,
band: p q,
record: record(x.T[x]),
so_lambda: 
x.t[x],
list: type List,
es-le: e loc e' ,
prop: 
,
natural_number: $n,
true: True,
guard: {T},
implies: P Q,
btrue: tt,
sq_type: SQType(T),
bool: 
,
es-E-interface: E(X),
uimplies: b supposing a,
real: 
,
grp_car: |g|,
eclass-val: X(e),
int: 
,
nat: 
,
bag-size: bag-size(bs),
eq_int: (i = j),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
es-loc: loc(e),
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
es-base-E: es-base-E(es),
token: "$token",
ifthenelse: if b then t else f fi ,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
assert: 
b,
record-select: r.x,
Id: Id,
set: {x:A| B[x]} ,
es-filter-image: f[X],
in-eclass: e X,
es-le-before: loc(e),
filter: filter(P;l),
eclass-events: eclass-events(es;X;L),
es-interface-predecessors: (X)(e),
lambda: x.A[x],
subtype: S T,
all: x:A. B[x],
equal: s = t,
event_ordering: EO,
es-E: E,
sqequal: s ~ t,
universe: Type,
bag: bag(T),
function: x:A B[x],
event-ordering+: EO+(Info),
uall: [x:A]. B[x],
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
member: t T,
isect: x:A. B[x],
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
cand: A c B,
l_contains: A B,
reducible: reducible(a),
prime: prime(a),
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
es-causl: (e < e'),
es-locl: (e <loc e'),
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
rev_uimplies: rev_uimplies(P;Q)
Lemmas :
assert_of_eq_int,
eq_int_eq_true,
es-is-filter-image,
sq_stable_from_decidable,
decidable__false,
eclass_wf,
member_wf,
in-eclass_wf,
assert_elim,
bool_wf,
bool_subtype_base,
subtype_base_sq,
assert_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
es-E_wf,
eclass-val_wf,
nat_wf,
bag-size_wf,
eq_int_wf,
Id_wf,
es-loc_wf,
es-interface-top,
filter-filter,
es-le-before_wf,
bag_wf,
filter_wf,
list_subtype_base,
set_subtype_base,
band_wf,
filter-sq,
l_member_wf,
es-filter-image_wf,
top_wf,
property-from-l_member,
sq_stable_wf,
sq_stable__equal,
es-le-before_wf2,
es-le_wf,
es-le-loc,
uiff_wf,
assert-eq-id,
permutation_wf,
subtype_rel_wf,
true_wf,
squash_wf,
subtype_rel_bag,
eqtt_to_assert,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
bfalse_wf,
false_wf,
ifthenelse_wf,
iff_wf,
rev_implies_wf,
sq_stable__iff,
sq_stable__assert,
sq_stable__all,
assert_witness,
intensional-universe_wf
\mforall{}[Info,A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
(\mleq{}(f[X])(e) \msim{} filter(\mlambda{}e.(bag-size(f X(e)) =\msubz{} 1);\mleq{}(X)(e)))
Date html generated:
2011_08_16-PM-05_22_37
Last ObjectModification:
2011_06_20-AM-01_22_00
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