{ 
es:EO. p:E 
(E + Top).
(causal-predecessor(es;p) 
(e,e':E. (e p
e' e c e'))) }
{ Proof }
Definitions occuring in Statement :
es-p-le: e p e',
causal-predecessor: causal-predecessor(es;p),
es-causle: e c 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 :
member: t 
T,
equal: s = t,
es-E: E,
function: x:A B[x],
event_ordering: EO,
causal-predecessor: causal-predecessor(es;p),
all: x:A. B[x],
es-causl: (e < e'),
universe: Type,
prop: 
,
union: left + right,
pair: <a, b>,
dep-isect: Error :dep-isect,
record-select: r.x,
infix_ap: x f y,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
apply: f a,
implies: P Q,
assert: 
b,
top: Top,
bool: 
,
guard: {T},
or: P 
Q,
subtype_rel: A 
r B,
strong-subtype: strong-subtype(A;B),
es-causle: e c e',
es-p-locl: e p< e',
not: 
A,
p-graph: p-graph(A;f),
product: x:A 
B[x],
exists: 
x:A. B[x],
void: Void,
false: False,
eclass: Error :eclass,
fpf: a:A fp-> B[a],
limited-type: LimitedType,
decidable: Dec(P),
es-locl: (e <loc e'),
es-le: e loc 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),
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),
es-p-le: e p e'
Lemmas :
es-causl_weakening_p-locl,
es-causle_wf,
es-p-le_wf,
causal-predecessor_wf,
top_wf,
event_ordering_wf,
decidable__es-causl,
es-E_wf,
es-causl_wf
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top). (causal-predecessor(es;p) {}\mRightarrow{} (\mforall{}e,e':E. (e p\mleq{} e' {}\mRightarrow{} e c\mleq{} e')))
Date html generated:
2011_08_16-AM-11_16_21
Last ObjectModification:
2010_09_24-PM-08_44_50
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