{ 
es:EO. e,e':E. ((e' 
es-pred-list(es;e)) 
(e' < e)) }
{ Proof }
Definitions occuring in Statement :
es-pred-list: es-pred-list(es;e),
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
all: x:A. B[x],
iff: P Q,
l_member: (x l)
Definitions :
es-pred-list: es-pred-list(es;e),
iff: P Q,
product: x:A 
B[x],
event_ordering: EO,
es-E: E,
all: x:A. B[x],
function: x:A 
B[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
equal: s = t,
es-base-E: es-base-E(es),
token: "$token",
record-select: r.x,
apply: f a,
pi1: fst(t),
l_member: (x l),
es-causl: (e < e'),
implies: P Q,
list: type List,
member: t T,
and: P 
Q,
pair: <a, b>,
guard: {T},
decide: case b of inl(x) => s[x] | inr(y) => t[y],
cand: A c B,
so_lambda: 
x.t[x],
real: 
,
grp_car: |g|,
subtype: S 
T,
int: 
,
limited-type: LimitedType,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
uiff: uiff(P;Q),
intensional-universe: IType,
fpf: a:A fp-> B[a],
set: {x:A| B[x]} ,
assert: 
b,
subtype_rel: A r B,
eq_atom: eq_atom$n(x;y),
bool: 
,
prop: 
,
less_than: a < b,
nat: 
,
not: 
A,
exists: 
x:A. B[x],
infix_ap: x f y,
union: left + right,
or: P 
Q,
Id: Id,
uimplies: b supposing a,
dep-isect: Error :dep-isect,
record+: record+,
record: record(x.T[x]),
atom: Atom,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
universe: Type,
top: Top,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
suptype: suptype(S; T),
rev_implies: P Q,
es-bcausl: es-bcausl(es;e;e'),
lambda: x.A[x],
es-dom: es-dom(es),
sqequal: s ~ t,
filter: filter(P;l),
Complete: Error :Complete,
Try: Error :Try,
append: as @ bs,
map: map(f;as),
cons: [car / cdr],
hd: hd(l),
last: last(L),
remove-repeats: remove-repeats(eq;L),
select: l[i],
so_apply: x[s],
MaAuto: Error :MaAuto,
THENM: Error :THENM,
CollapseTHENM: Error :CollapseTHENM,
true: True,
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,
squash: 
T,
fpf-sub: f g,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
sq_stable: SqStable(P),
rnonneg: rnonneg(r),
false: False,
nil: [],
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
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),
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,
decidable: Dec(P),
void: Void
Lemmas :
assert_witness,
true_wf,
ifthenelse_wf,
false_wf,
list-subtype,
decidable__assert,
decidable_wf,
l_member_set2,
sq_stable__assert,
rev_implies_wf,
assert-es-bcausl,
and_functionality_wrt_iff,
iff_functionality_wrt_iff,
member_filter,
l_member_subtype,
filter_type,
es-bcausl_wf,
es-dom_wf,
filter_wf,
assert_wf,
filter-filter,
iff_wf,
es-causl_wf,
es-base-E_wf,
subtype_rel_self,
bool_wf,
intensional-universe_wf,
member_wf,
subtype_rel_wf,
not_wf,
Id_wf,
record-select_wf,
top_wf,
l_member_wf,
nat_wf,
es-E_wf,
event_ordering_wf
\mforall{}es:EO. \mforall{}e,e':E. ((e' \mmember{} es-pred-list(es;e)) \mLeftarrow{}{}\mRightarrow{} (e' < e))
Date html generated:
2011_08_16-AM-10_24_04
Last ObjectModification:
2010_11_22-PM-06_13_57
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