{ 
[Info:Type]. [es:EO+(Info)]. [A:Type]. [P:A 
]. [f:Top].
[X:EClass(A)]. [e:E].
uiff(
e 
(f[v] where v from X such that P[v]);(e X) 
(P[X(e)])) }
{ Proof }
Definitions occuring in Statement :
mapfilter-class: (f[v] where v from X such that P[v]),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
bool: ,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
top: Top,
so_apply: x[s],
and: P Q,
function: x:A B[x],
universe: Type
Definitions :
intensional-universe: IType,
tag-by: z
T,
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
list: type List,
fpf-cap: f(x)?z,
record: record(x.T[x]),
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,
squash: 
T,
sq_stable: SqStable(P),
cand: A c B,
cond-class: [X?Y],
union: left + right,
or: P 
Q,
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
fpf: a:A fp-> B[a],
es-E-interface: E(X),
so_lambda: 
x.t[x],
eclass-val: X(e),
strong-subtype: strong-subtype(A;B),
set: {x:A| B[x]} ,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
so_apply: x[s],
mapfilter-class: (f[v] where v from X such that P[v]),
in-eclass: e X,
rev_implies: P 
Q,
iff: P 
Q,
implies: P Q,
prop: 
,
pair: <a, b>,
false: False,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: b,
uimplies: b supposing a,
product: x:A B[x],
and: P Q,
uiff: uiff(P;Q),
bag: bag(T),
subtype: S T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
es-base-E: es-base-E(es),
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
void: Void,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
top: Top,
bool: ,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A B[x],
isect: x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
member: t T,
event-ordering+: EO+(Info),
equal: s = t,
tactic: Error :tactic,
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
eq_bool: p =b q,
empty-bag: {},
single-bag: {x},
bag-only: only(bs),
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
real: 
,
grp_car: |g|,
nat: 
,
limited-type: LimitedType,
btrue: tt,
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,
natural_number: $n,
bag-size: bag-size(bs),
eq_int: (i =
j),
bnot: b,
int: 
,
unit: Unit,
eclass-compose1: f o X,
es-filter-image: f[X],
MaAuto: Error :MaAuto,
Repeat: Error :Repeat,
CollapseTHEN: Error :CollapseTHEN,
RepUR: Error :RepUR,
Unfold: Error :Unfold,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA
Lemmas :
bag-size_wf,
nat_wf,
eq_int_wf,
not_wf,
bnot_wf,
assert_of_eq_int,
not_functionality_wrt_uiff,
assert_of_bnot,
uiff_transitivity,
eqff_to_assert,
eqtt_to_assert,
bag-only_wf,
assert_wf,
true_wf,
ifthenelse_wf,
false_wf,
in-eclass_wf,
assert_witness,
uiff_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
es-E_wf,
event-ordering+_wf,
eclass_wf,
top_wf,
bool_wf,
mapfilter-class_wf,
eclass-val_wf,
member_wf,
subtype_rel_wf,
es-interface-top,
rev_implies_wf,
iff_wf,
sq_stable__assert,
intensional-universe_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:Top]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (f[v] where v from X such that P[v]);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}P[X(e)]))
Date html generated:
2011_08_16-PM-04_14_11
Last ObjectModification:
2011_06_20-AM-00_44_01
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