{ 
[Info:Type]. [A:es:EO+(Info) 
e:E Type]. [R:es:EO+(Info)
e:E
A[es;e]
].
((es:EO+(Info). e:E. Dec(
a:A[es;e]. R[es;e;a]))
(X:EClass(A[es;e])
es:EO+(Info). e:E.
((
e 
X 
a:A[es;e]. R[es;e;a])
R[es;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],
so_apply: x[s1;s2],
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 :
eq_atom: eq_atom$n(x;y),
atom: Atom,
top: Top,
es-base-E: es-base-E(es),
token: "$token",
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
sq_stable: SqStable(P),
so_apply: x[s],
guard: {T},
l_member: (x l),
eclass-val: X(e),
rev_implies: P Q,
in-eclass: e X,
so_lambda: 
x.t[x],
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],
decidable: Dec(P),
all: x:A. B[x],
bag: bag(T),
quotient: x,y:A//B[x; y],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
prop: ,
universe: Type,
so_apply: x[s1;s2],
apply: f a,
es-E: E,
event_ordering: EO,
event-ordering+: EO+(Info),
implies: P Q,
exists: x:A. B[x],
product: x:A 
B[x],
eclass: EClass(A[eo; e]),
function: x:A B[x],
MaAuto: Error :MaAuto,
tactic: Error :tactic,
empty-bag: {},
pi1: fst(t),
single-bag: {x},
decide: case b of inl(x) => s[x] | inr(y) => t[y],
lambda: x.A[x],
inr: inr x ,
false: False,
pair: <a, b>,
inl: inl x ,
set: {x:A| B[x]} ,
limited-type: LimitedType,
Auto: Error :Auto,
Complete: Error :Complete,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor,
void: Void,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
cand: A c B,
bool: 
,
axiom: Ax,
natural_number: $n,
int: 
,
true: True,
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),
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',
bnot: b,
bimplies: p q,
band: p q,
bor: p q,
bag-only: only(bs),
real: 
,
grp_car: |g|,
nat: 
,
bag-size: bag-size(bs)
Lemmas :
eq_int_wf,
bag-only_wf,
assert_of_eq_int,
bag-size_wf,
nat_wf,
true_wf,
false_wf,
single-bag_wf,
empty-bag_wf,
iff_wf,
assert_wf,
eclass_wf,
event-ordering+_wf,
es-E_wf,
decidable_wf,
event-ordering+_inc,
uall_wf,
es-base-E_wf,
subtype_rel_self
\mforall{}[Info:Type]. \mforall{}[A:es:EO+(Info) {}\mrightarrow{} e:E {}\mrightarrow{} Type]. \mforall{}[R:es:EO+(Info) {}\mrightarrow{} e:E {}\mrightarrow{} A[es;e] {}\mrightarrow{} \mBbbP{}].
((\mforall{}es:EO+(Info). \mforall{}e:E. Dec(\mexists{}a:A[es;e]. R[es;e;a]))
{}\mRightarrow{} (\mexists{}X:EClass(A[es;e])
\mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mexists{}a:A[es;e]. R[es;e;a]) \mwedge{} R[es;e;X(e)] supposing \muparrow{}e \mmember{}\msubb{} X)))
Date html generated:
2011_08_16-PM-04_39_12
Last ObjectModification:
2011_06_20-AM-01_01_27
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