{ 
es:EO. p:E 
(E + Top).
(causal-predecessor(es;p) 
(e,e':E. (e p< e' (e < e')))) }
{ Proof }
Definitions occuring in Statement :
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
top: Top,
all: x:A. B[x],
implies: P Q,
function: x:A B[x],
union: left + right
Definitions :
equal: s = t,
member: t 
T,
function: x:A B[x],
all: x:A. B[x],
event_ordering: EO,
top: Top,
union: left + right,
es-E: E,
causal-predecessor: causal-predecessor(es;p),
es-p-locl: e p< e',
es-causl: (e < e'),
subtype_rel: A 
r B,
strong-subtype: strong-subtype(A;B),
product: x:A 
B[x],
p-graph: p-graph(A;f),
exists: 
x:A. B[x],
apply: f a,
record-select: r.x,
infix_ap: x f y,
assert: 
b,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
prop: 
,
implies: P Q,
nat_plus: 
,
guard: {T},
sq_type: SQType(T),
natural_number: $n,
int: 
,
less_than: a < b,
or: P 
Q,
decidable: Dec(P),
set: {x:A| B[x]} ,
list: type List,
nat: ,
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_disjoint: l_disjoint(T;l1;l2),
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
limited-type: LimitedType,
atom: Atom$n,
rationals: 
,
qle: r 
s,
qless: r < s,
q-rel: q-rel(r;x),
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),
string: Error :string,
Id: Id,
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
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-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],
es-fset-loc: i locs(s),
es-E-interface: Error :es-E-interface,
collect-event: Error :collect-event,
cut-order: Error :cut-order,
path-goes-thru: Error :path-goes-thru,
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
le: A B,
universe: Type,
void: Void,
false: False,
not: 
A,
subtype: S T,
real: 
,
p-fun-exp: f^n,
add: n + m,
lambda: 
x.A[x],
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
p-compose: f o g,
p-id: p-id(),
isect: 
x:A. B[x],
suptype: suptype(S; T),
subtract: n - m,
cand: A c
B,
and: P Q,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
minus: -n,
pair: <a, b>,
bool: 
,
true: True,
rev_implies: P 
Q,
iff: P Q,
sqequal: s ~ t,
bfalse: ff,
bnot: 
b,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
set_blt: a < b,
grp_blt: a < b,
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
eq_type: eq_type(T;T'),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
eq_str: Error :eq_str,
bimplies: p q,
band: p q,
bor: p q,
btrue: tt
Lemmas :
es-causl_transitivity2,
es-causle_weakening,
bool_cases,
eqtt_to_assert,
bool_sq,
iff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
not_wf,
p-compose_wf,
p-fun-exp-add,
iff_wf,
rev_implies_wf,
bool_wf,
squash_wf,
true_wf,
p-fun-exp-one,
can-apply-fun-exp,
nat_wf,
assert_wf,
can-apply_wf,
do-apply_wf,
member_wf,
nat_plus_properties,
p-graph_wf,
p-graph_wf2,
p-fun-exp_wf,
le_wf,
decidable__equal_int,
int_sq,
es-causl_wf,
es-p-locl_wf,
causal-predecessor_wf,
es-E_wf,
top_wf,
event_ordering_wf
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top). (causal-predecessor(es;p) {}\mRightarrow{} (\mforall{}e,e':E. (e p< e' {}\mRightarrow{} (e < e'))))
Date html generated:
2011_08_16-AM-11_16_11
Last ObjectModification:
2010_09_24-PM-08_44_56
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