{ 
[Info:Type]. [es:EO+(Info)]. [A,B:Type]. [X:EClass(A)]. [P:B 
].
[num:A 
]. [init:B]. [f:B A B]. [e:E].
uiff(
e 
es-collect-accum(X;x.num[x];init;b,v.f[b;v];b.P[b]);(e X)
e is first@ loc(e) s.t.
c.collect-event(es;X;num[X(e)];v.num[v];L.P[list_accum(b,v.f[b;v];
init;
L)];c)
e'<e.(e' X) 
(num[X(e')] 
num[X(e)])) }
{ Proof }
Definitions occuring in Statement :
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: e<e'.P[e],
es-loc: loc(e),
es-E: E,
assert: b,
bool: ,
nat: ,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
le: A B,
implies: P Q,
and: P Q,
function: x:A B[x],
universe: Type,
list_accum: list_accum(x,a.f[x; a];y;l)
Definitions :
nat_plus: 
,
l_contains: A 
B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
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,
dstype: dstype(TypeNames; d; a),
fset-member: a s,
f-subset: xs ys,
fset: FSet{T},
fset-closed: (s closed under fs),
IdLnk: IdLnk,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
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,
consensus-rcv: consensus-rcv(V;A),
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.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],
es-fset-loc: i locs(s),
exists: x:A. B[x],
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
limited-type: LimitedType,
permutation: permutation(T;L1;L2),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
bag-size: bag-size(bs),
fpf-sub: f g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
fpf-cap: f(x)?z,
label: ...$L... t,
rev_implies: P 
Q,
es-filter-image: f[X],
squash: 
T,
iff: P Q,
cand: A c B,
quotient: x,y:A//B[x; y],
infix_ap: x f y,
es-causl: (e < e'),
eq_knd: a = b,
fpf-dom: x dom(f),
intensional-universe: IType,
unit: Unit,
bfalse: ff,
int_eq: if a=b then c else d,
btrue: tt,
atom_eq: atomeqn def,
sq_type: SQType(T),
sqequal: s ~ t,
rationals: 
,
or: P 
Q,
append: as @ bs,
guard: {T},
locl: locl(a),
Knd: Knd,
atom: Atom$n,
filter: filter(P;l),
l_member: (x l),
union: left + right,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
fpf: a:A fp-> B[a],
real: 
,
grp_car: |g|,
subtype: S T,
subtype_rel: A r B,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
es-E-interface: E(X),
es-interface-predecessors: (X)(e),
eq_int: (i =
j),
mapfilter: mapfilter(f;P;L),
top: Top,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
bag: bag(T),
record-select: r.x,
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
in-eclass: e X,
es-locl: (e <loc e'),
eclass-val: X(e),
apply: f a,
axiom: Ax,
es-loc: loc(e),
Id: Id,
prop: 
,
event_ordering: EO,
es-E: E,
bool: ,
so_lambda: 
x y.t[x; y],
event-ordering+: EO+(Info),
universe: Type,
uall: [x:A]. B[x],
uiff: uiff(P;Q),
es-first-at: e is first@ i s.t. e.P[e],
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
alle-lt: e<e'.P[e],
all: x:A. B[x],
le: A B,
not: 
A,
implies: P Q,
function: x:A B[x],
false: False,
void: Void,
uimplies: b supposing a,
isect: 
x:A. B[x],
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
member: t T,
equal: s = t,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
so_apply: x[s1;s2],
list_accum: list_accum(x,a.f[x; a];y;l),
so_apply: x[s],
es-collect: Collect(X;x.num[x];L.P[L]),
pi2: snd(t),
pi1: fst(t),
pair: <a, b>,
single-bag: {x},
lambda: x.A[x],
int: 
,
product: x:A 
B[x],
assert: b,
length: ||as||,
natural_number: $n,
less_than: a < b,
and: P Q,
list: type List,
set: {x:A| B[x]} ,
so_lambda: x.t[x],
nat: ,
eclass: EClass(A[eo; e]),
tactic: Error :tactic,
Try: Error :Try
Lemmas :
le_wf,
assert_wf,
es-locl_wf,
es-E_wf,
collect-event_wf,
assert_witness,
nat_wf,
bool_wf,
eclass_wf,
es-first-at_wf,
alle-lt_wf,
event-ordering+_wf,
in-eclass_wf,
member_wf,
es-interface-top,
eclass-val_wf,
es-interface-predecessors_wf,
Id_wf,
es-E-interface_wf,
mapfilter_wf,
list_accum_wf,
es-loc_wf,
es-base-E_wf,
subtype_rel_self,
event-ordering+_inc,
eq_int_wf,
subtype_rel_wf,
false_wf,
ifthenelse_wf,
true_wf,
list-subtype,
l_member_wf,
uiff_wf,
assert-eq-id,
subtype_base_sq,
bool_subtype_base,
assert_elim,
btrue_wf,
bfalse_wf,
unit_wf,
intensional-universe_wf,
es-interface-val_wf2,
length_wf1,
es-collect-accum_wf,
es-interface-subtype_rel2,
top_wf,
uiff_functionality_wrt_uiff2,
iff_weakening_uiff,
assert_functionality_wrt_uiff,
squash_wf,
es-collect-accum-es-collect,
iff_wf,
rev_implies_wf,
es-collect_wf,
pi1_wf,
pi2_wf,
single-bag_wf,
es-filter-image_wf,
es-interface-subtype_rel,
es-is-filter-image,
pi1_wf_top,
subtype_rel_simple_product,
bag-size_wf,
permutation_wf,
bag_wf,
and_functionality_wrt_uiff2,
is-es-collect,
decidable_wf,
decidable__equal_int
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:B {}\mrightarrow{} \mBbbB{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[init:B].
\mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} es-collect-accum(X;x.num[x];init;b,v.f[b;v];b.P[b]);(\muparrow{}e \mmember{}\msubb{} X)
\mwedge{} e is first@ loc(e) s.t. c.collect-event(es;X;num[X(e)];v.num[v];L.P[list\_accum(b,v.f[b;v];
init;
L)];c)
\mwedge{} \mforall{}e'<e.(\muparrow{}e' \mmember{}\msubb{} X) {}\mRightarrow{} (num[X(e')] \mleq{} num[X(e)]))
Date html generated:
2011_08_16-PM-05_28_03
Last ObjectModification:
2011_06_20-AM-01_24_07
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