{ 
[Info:Type]. [es:EO+(Info)]. [A,B:Type]. [f:A 
bag(B)]. [X:EClass(A)].
[e:E].
uiff(
e 
f[X];(e X) 
(bag-size(f X(e)) = 1)) }
{ Proof }
Definitions occuring in Statement :
es-filter-image: f[X],
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
and: P Q,
apply: f a,
function: x:A B[x],
natural_number: $n,
int: 
,
universe: Type,
equal: s = t,
bag-size: bag-size(bs),
bag: bag(T)
Definitions :
rationals: 
,
so_apply: x[s],
or: P 
Q,
l_member: (x l),
limited-type: LimitedType,
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i 
z j,
eq_int: (i =
j),
null: null(as),
set_blt: a < b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p 
q,
band: p q,
bor: p q,
bnot: 
b,
unit: Unit,
sqequal: s ~ t,
lambda: 
x.A[x],
real: 
,
grp_car: |g|,
nat: 
,
cand: A c B,
fpf-sub: f 
g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
fpf-dom: x dom(f),
guard: {T},
squash: 
T,
fpf-cap: f(x)?z,
permutation: permutation(T;L1;L2),
list: type List,
quotient: x,y:A//B[x; y],
union: left + right,
fpf: a:A fp-> B[a],
intensional-universe: IType,
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: A,
less_than: a < b,
es-E-interface: E(X),
subtype_rel: A r B,
subtype: S T,
suptype: suptype(S; T),
bool: 
,
top: Top,
all: x:A. B[x],
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
set: {x:A| B[x]} ,
record-select: r.x,
es-filter-image: f[X],
axiom: Ax,
natural_number: $n,
eclass-val: X(e),
apply: f a,
bag-size: bag-size(bs),
int: ,
implies: P Q,
prop: 
,
pair: <a, b>,
event_ordering: EO,
es-E: E,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
uiff: uiff(P;Q),
and: P Q,
product: x:A 
B[x],
uimplies: b supposing a,
assert: b,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
equal: s = t,
false: False,
void: Void,
event-ordering+: EO+(Info),
universe: Type,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
function: x:A B[x],
bag: bag(T),
MaAuto: Error :MaAuto,
in-eclass: e X,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
bag_wf,
top_wf,
member_wf,
es-filter-image_wf,
in-eclass_wf,
assert_wf,
es-interface-top,
eclass_wf,
assert_witness,
es-E_wf,
event-ordering+_wf,
intensional-universe_wf,
subtype_rel_wf,
permutation_wf,
true_wf,
squash_wf,
es-base-E_wf,
subtype_rel_self,
subtype_rel_bag,
bag-size_wf,
nat_wf,
eclass-val_wf,
event-ordering+_inc,
is-filter-image-sq,
bool_wf,
eqtt_to_assert,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
assert_of_eq_int,
eq_int_wf,
false_wf,
ifthenelse_wf,
assert_elim,
eq_int_eq_true,
uiff_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} f[X];(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (bag-size(f X(e)) = 1))
Date html generated:
2011_08_16-PM-04_11_22
Last ObjectModification:
2011_06_20-AM-00_43_21
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