{ 
[Info:Type]
es:EO+(Info). X:EClass(Top). f:sys-antecedent(es;X). s:FSet{E(X)}.
c:Cut(X;f). (s 
c 
([c':Cut(X;f)]. c c' supposing s c')) }
{ Proof }
Definitions occuring in Statement :
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-eq: es-eq(es),
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
exists: x:A. B[x],
and: P Q,
universe: Type,
fset: FSet{s},
f-subset: xs ys
Definitions :
fset-union: x 
y,
so_apply: x[s],
or: P 
Q,
guard: {T},
l_member: (x 
l),
void: Void,
false: False,
true: True,
apply: f a,
es-causle: e c
e',
implies: P 
Q,
cand: A c B,
fpf: a:A fp-> B[a],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
fset-member: a s,
tl: tl(l),
hd: hd(l),
l_all: (xL.P[x]),
set-equal: set-equal(T;x;y),
prop: 
,
fset-closed: (s closed under fs),
fset-closure: (c = fs closure of s),
es-eq: es-eq(es),
list: type List,
union: left + right,
subtype: S T,
top: Top,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
equal: s = t,
member: t T,
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
quotient: x,y:A//B[x; y],
dep-isect: Error :dep-isect,
record+: record+,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A r B,
so_lambda: 
x y.t[x; y],
all: x:A. B[x],
function: x:A 
B[x],
es-E-interface: E(X),
es-cut: Cut(X;f),
set: {x:A| B[x]} ,
fset: FSet{T},
sys-antecedent: sys-antecedent(es;Sys),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
universe: Type,
exists: x:A. B[x],
and: P Q,
product: x:A 
B[x],
uall: [x:A]. B[x],
so_lambda: x.t[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
f-subset: xs ys,
nil: [],
es-interface-pred: X-pred,
cons: [car / cdr],
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,
infix_ap: x f y,
es-causl: (e < e'),
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),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
decidable: Dec(P),
iff: P 
Q,
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
Lemmas :
sq_stable_from_decidable,
decidable__fset-closed,
es-cut_wf,
f-subset_wf,
es-E-interface_wf,
uall_wf,
sys-antecedent_wf,
es-interface-pred_wf,
sys-antecedent-closure,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
top_wf,
eclass_wf,
fset_wf,
member_wf,
set-equal_wf,
subtype_rel_wf,
es-eq_wf-interface,
fset-closed_wf,
es-interface-pred_wf2,
fset-member_wf,
fset-member_witness,
uiff_inversion,
l_all_wf,
l_member_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}s:FSet\{E(X)\}.
\mexists{}c:Cut(X;f). (s \msubseteq{} c \mwedge{} (\mforall{}[c':Cut(X;f)]. c \msubseteq{} c' supposing s \msubseteq{} c'))
Date html generated:
2011_08_16-PM-05_46_19
Last ObjectModification:
2011_06_20-AM-01_33_36
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