{ 
es:EO
[R:{R:E 
E 
| e,e':E. (R[e;e'] 
(e' < e))} ]
((e,e':E. Dec(R[e;e']))
(
p:E (E + Top)
(causal-predecessor(es;p)
(e:E
((
can-apply(p;e) 
e':E. R[e;e'])
R[e;do-apply(p;e)] supposing can-apply(p;e)))))) }
{ Proof }
Definitions occuring in Statement :
causal-predecessor: causal-predecessor(es;p),
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
assert: b,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
prop: ,
so_apply: x[s1;s2],
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
union: left + right,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x)
Definitions :
strong-subtype: strong-subtype(A;B),
equal: s = t,
member: t 
T,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record-select: r.x,
infix_ap: x f y,
dep-isect: Error :dep-isect,
record+: record+,
subtype_rel: A 
r B,
top: Top,
causal-predecessor: causal-predecessor(es;p),
iff: P Q,
assert: b,
uimplies: b supposing a,
and: P Q,
or: P 
Q,
event_ordering: EO,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
es-causl: (e < e'),
universe: Type,
set: {x:A| B[x]} ,
implies: P Q,
apply: f a,
prop: ,
product: x:A 
B[x],
union: left + right,
function: x:A B[x],
so_apply: x[s1;s2],
es-E: E,
exists: x:A. B[x],
decidable: Dec(P),
all: x:A. B[x],
lambda: 
x.A[x],
so_lambda: 
x.t[x],
es-le: e loc e' ,
es-causle: e c e',
es-locl: (e <loc e'),
record: record(x.T[x]),
cand: A c B,
false: False,
guard: {T},
true: True,
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),
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
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,
squash: 
T,
fpf-sub: f g,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
sq_stable: SqStable(P),
i-member: r I,
do-apply: do-apply(f;x),
suptype: suptype(S; T),
can-apply: can-apply(f;x),
limited-type: LimitedType,
fpf: a:A fp-> B[a],
list: type List,
void: Void,
unit: Unit,
subtype: S T,
it: 
,
inr: inr x ,
pi1: fst(t),
inl: inl x ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
rev_implies: P Q,
pair: <a, b>,
bool: 
,
axiom: Ax,
natural_number: $n,
int: 
,
outl: outl(x)
Lemmas :
true_wf,
member_wf,
pi1_wf_top,
subtype_rel_wf,
unit_wf,
it_wf,
can-apply_wf,
do-apply_wf,
sq_stable_from_decidable,
decidable__es-causl,
not_wf,
false_wf,
decidable__existse-causl,
assert_wf,
iff_wf,
causal-predecessor_wf,
top_wf,
decidable_wf,
es-E_wf,
es-causl_wf,
event_ordering_wf
\mforall{}es:EO
\mforall{}[R:\{R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}| \mforall{}e,e':E. (R[e;e'] {}\mRightarrow{} (e' < e))\} ]
((\mforall{}e,e':E. Dec(R[e;e']))
{}\mRightarrow{} (\mexists{}p:E {}\mrightarrow{} (E + Top)
(causal-predecessor(es;p)
\mwedge{} (\mforall{}e:E
((\muparrow{}can-apply(p;e) \mLeftarrow{}{}\mRightarrow{} \mexists{}e':E. R[e;e'])
\mwedge{} R[e;do-apply(p;e)] supposing \muparrow{}can-apply(p;e))))))
Date html generated:
2011_08_16-AM-11_12_56
Last ObjectModification:
2011_06_20-AM-00_20_35
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