{ 
[Info,A:Type]. [P:eo:EO+(Info) 
E A 
].
((eo:EO+(Info). e:E. Dec(
a:A. P[eo;e;a]))
(X:EClass(A)
eo:EO+(Info). e:E.
((
e 
X 
a:A. P[eo;e;a]) 
P[eo;e;X(e)] supposing e X))) }
{ Proof }
Definitions occuring in Statement :
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2;s3],
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
implies: P Q,
and: P Q,
function: x:A B[x],
universe: Type
Definitions :
intensional-universe: IType,
so_lambda: 
x.t[x],
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,
bool: 
,
record: record(x.T[x]),
es-E-interface: E(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),
cond-class: [X?Y],
so_apply: x[s],
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
cand: A c B,
fpf: a:A fp-> B[a],
set: {x:A| B[x]} ,
false: False,
true: True,
eclass-val: X(e),
rev_implies: P Q,
in-eclass: e X,
eq_atom: eq_atom$n(x;y),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-select: r.x,
inr: inr x ,
void: Void,
pair: <a, b>,
inl: inl x ,
top: Top,
dep-isect: Error :dep-isect,
record+: record+,
subtype: S T,
equal: s = t,
member: t T,
strong-subtype: strong-subtype(A;B),
union: left + right,
or: P 
Q,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A r B,
so_lambda: x y.t[x; y],
iff: P Q,
assert: b,
uimplies: b supposing a,
and: P Q,
so_apply: x[s1;s2;s3],
uall: [x:A]. B[x],
isect: x:A. B[x],
es-E: E,
event_ordering: EO,
event-ordering+: EO+(Info),
exists: x:A. B[x],
product: x:A B[x],
eclass: EClass(A[eo; e]),
bag: bag(T),
quotient: x,y:A//B[x; y],
prop: ,
universe: Type,
implies: P Q,
all: x:A. B[x],
function: x:A B[x],
decidable: Dec(P),
empty-bag: {},
pi1: fst(t),
single-bag: {x},
apply: f a,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
lambda: x.A[x],
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
axiom: Ax,
natural_number: $n,
int: 
,
eq_int: (i =
j),
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
limited-type: LimitedType,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
RepUR: Error :RepUR,
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor,
tactic: Error :tactic
Lemmas :
not_wf,
eclass_wf,
member_wf,
in-eclass_wf,
assert_wf,
assert_witness,
es-E_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
empty-bag_wf,
pi1_wf_top,
single-bag_wf,
iff_wf,
decidable_wf,
false_wf,
ifthenelse_wf,
true_wf,
rev_implies_wf,
top_wf,
sq_stable__assert,
bool_wf,
subtype_rel_wf,
intensional-universe_wf,
es-interface-top,
eclass-val_wf
\mforall{}[Info,A:Type]. \mforall{}[P:eo:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}].
((\mforall{}eo:EO+(Info). \mforall{}e:E. Dec(\mexists{}a:A. P[eo;e;a]))
{}\mRightarrow{} (\mexists{}X:EClass(A)
\mforall{}eo:EO+(Info). \mforall{}e:E. ((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mexists{}a:A. P[eo;e;a]) \mwedge{} P[eo;e;X(e)] supposing \muparrow{}e \mmember{}\msubb{} X)))
Date html generated:
2011_08_16-PM-04_07_30
Last ObjectModification:
2011_06_20-AM-00_41_14
Home
Index