{ 
[Info,A:Type]. [P:A 
]. [X:EClass(A)].
(X 
EClass({a:A| P[a]} )) supposing
((es:EO+(Info). e:E(X). P[X(e)]) and
Singlevalued(X)) }
{ Proof }
Definitions occuring in Statement :
es-E-interface: E(X),
sv-class: Singlevalued(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: x:A. B[x],
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
universe: Type
Definitions :
guard: {T},
implies: P 
Q,
btrue: tt,
sq_type: SQType(T),
bool: 
,
true: True,
in-eclass: e 
X,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
record+: record+,
subtype: S 
T,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
eclass-val: X(e),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
void: Void,
false: False,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
axiom: Ax,
set: {x:A| B[x]} ,
event-ordering+: EO+(Info),
top: Top,
es-E-interface: E(X),
apply: f a,
so_apply: x[s],
all: x:A. B[x],
equal: s = t,
universe: Type,
function: x:A B[x],
uall: [x:A]. B[x],
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
so_lambda: 
x y.t[x; y],
prop: ,
sv-class: Singlevalued(X),
isect: 
x:A. B[x],
member: t T,
quotient: x,y:A//B[x; y],
record-select: r.x,
suptype: suptype(S; T),
natural_number: $n,
bag-size: bag-size(bs),
AssertBY: Error :AssertBY,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
bag: bag(T),
Complete: Error :Complete,
Try: Error :Try,
intensional-universe: IType,
so_lambda: x.t[x],
token: "$token",
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),
tag-by: zT,
rev_implies: P 
Q,
iff: P Q,
record: record(x.T[x]),
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 T2,
b-union: A 
B,
fpf-cap: f(x)?z,
real: 
,
grp_car: |g|,
nat: 
,
null: null(as),
set_blt: a < b,
grp_blt: a < b,
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,
int: 
,
permutation: permutation(T;L1;L2),
list: type List,
bag-only: only(bs),
eq_int: (i =
j),
union: left + right,
or: P Q,
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
cand: A c B,
l_member: (x l),
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
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,
infix_ap: x f y,
es-causl: (e < e'),
es-locl: (e <loc e'),
es-le: 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],
same-thread: same-thread(es;p;e;e'),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
es-fset-loc: i locs(s),
decidable: Dec(P),
exists: x:A. B[x],
RepUR: Error :RepUR,
RepeatFor: Error :RepeatFor,
MaAuto: Error :MaAuto,
CollapseTHENA: Error :CollapseTHENA,
sqequal: s ~ t,
nequal: a 
b T ,
tactic: Error :tactic,
deq: EqDecider(T),
ma-state: State(ds),
atom: Atom,
es-base-E: es-base-E(es),
fpf-dom: x dom(f),
pair: <a, b>,
class-program: ClassProgram(T)
Lemmas :
squash_wf,
nequal_wf,
es-base-E_wf,
subtype_rel_self,
neg_assert_of_eq_int,
subtype-bag-empty,
subtype_rel_bag,
subtype-bag-only,
bag-size_wf,
nat_wf,
le_wf,
eq_int_wf,
assert_of_eq_int,
bag-only_wf,
permutation_wf,
decidable__assert,
sq_stable__assert,
intensional-universe_wf,
not_wf,
bag_wf,
eclass_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
sv-class_wf,
in-eclass_wf,
assert_elim,
bool_wf,
bool_subtype_base,
subtype_base_sq,
true_wf,
ifthenelse_wf,
false_wf,
assert_wf,
member_wf,
es-interface-top,
subtype_rel_wf,
eclass-val_wf,
es-E-interface_wf
\mforall{}[Info,A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[X:EClass(A)].
(X \mmember{} EClass(\{a:A| P[a]\} )) supposing ((\mforall{}es:EO+(Info). \mforall{}e:E(X). P[X(e)]) and Singlevalued(X))
Date html generated:
2011_08_16-PM-04_08_19
Last ObjectModification:
2011_06_20-AM-00_41_40
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