{ 
[Info:Type]
es:EO+(Info). X:EClass(Top). f:sys-antecedent(es;X). a,b:E(X).
(a 
(X;f) b
(a = b)
((f b < b) 
a (X;f) f b)
((
b 
prior(X)) a (X;f) prior(X)(b))) }
{ Proof }
Definitions occuring in Statement :
cut-order: a (X;f) b,
es-prior-interface: prior(X),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-causl: (e < e'),
assert: b,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
iff: P Q,
or: P Q,
and: P Q,
apply: f a,
universe: Type,
equal: s = t
Definitions :
cut-order: a (X;f) b,
subtype: S 
T,
top: Top,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
uall: [x:A]. B[x],
isect: 
x:A. B[x],
so_lambda: 
x y.t[x; y],
all: x:A. B[x],
iff: P Q,
and: P Q,
product: x:A 
B[x],
implies: P Q,
function: x:A 
B[x],
or: P Q,
union: left + right,
es-E-interface: E(X),
sys-antecedent: sys-antecedent(es;Sys),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
universe: Type,
equal: s = t,
member: t T,
es-eq-E: e = e',
void: Void,
es-causle: e c e',
infix_ap: x f y,
intensional-universe: IType,
es-eq: es-eq(es),
record: record(x.T[x]),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
cand: A c B,
false: False,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
dep-isect: Error :dep-isect,
record+: record+,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
set: {x:A| B[x]} ,
record-select: r.x,
subtype_rel: A r B,
uimplies: b supposing a,
eclass-val: X(e),
es-prior-interface: prior(X),
in-eclass: e X,
apply: f a,
limited-type: LimitedType,
true: True,
squash: 
T,
prop: 
,
rev_implies: P Q,
fset-singleton: {x},
fset-union: x 
y,
ifthenelse: if b then t else f fi ,
es-causl: (e < e'),
assert: b,
fset-member: a s,
cut-of: cut(X;f;s),
fset: FSet{T},
es-cut: Cut(X;f),
append: as @ bs,
locl: locl(a),
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,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
sq_stable: SqStable(P),
fset-filter: {x s | P[x]},
fset-intersection: a b,
fset-remove: fset-remove(eq;y;s),
fset-add: fset-add(eq;x;s),
axiom: Ax,
natural_number: $n,
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
so_apply: x[s],
l_member: (x l),
label: ...$L... t,
f-subset: xs ys,
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,
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),
exists: x:A. B[x],
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),
nil: [],
es-interface-pred: X-pred,
cons: [car / cdr],
fset-closed: (s closed under fs),
fpf-cap: f(x)?z,
filter: filter(P;l),
set-equal: set-equal(T;x;y),
list: type List,
quotient: x,y:A//B[x; y],
deq: EqDecider(T),
guard: {T},
sq_type: SQType(T),
pair: <a, b>,
bfalse: ff,
btrue: tt,
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,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
bimplies: p q,
band: p q,
bor: p q,
bnot: b,
bool: 
,
unit: Unit,
int: 
Lemmas :
iff_weakening_uiff,
bool_wf,
bnot_wf,
not_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
assert-es-eq-E-2,
not_functionality_wrt_uiff,
es-eq-E_wf,
iff_functionality_wrt_iff,
member-fset-union,
or_functionality_wrt_uiff2,
member-fset-singleton,
es-eq_wf-interface,
set-equal_wf,
fset-closed_wf,
es-interface-pred_wf2,
decidable_wf,
decidable__fset-member,
es-causl_transitivity2,
es-causl_irreflexivity,
es-causle_wf,
es-causle_weakening_eq,
uiff_inversion,
decidable__equal_es-E-interface,
fset-member_witness,
deq-member_wf,
iff_transitivity,
or_functionality_wrt_iff,
sq_stable_from_decidable,
decidable__es-causle,
es-causl_wf,
fset-member_wf,
cut-of_wf,
iff_wf,
ifthenelse_wf,
fset_wf,
fset-union_wf,
fset-singleton_wf,
assert_wf,
rev_implies_wf,
true_wf,
squash_wf,
es-cut_wf,
fset-member_wf-cut,
cut-of-singleton,
es-prior-interface_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-prior-interface_wf1,
eclass-val_wf2,
member_wf,
subtype_rel_wf,
false_wf,
es-base-E_wf,
subtype_rel_self,
intensional-universe_wf,
es-E-interface-subtype_rel,
es-interface-subtype_rel2,
es-E-interface_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X). \mforall{}a,b:E(X).
(a \mleq{}(X;f) b
\mLeftarrow{}{}\mRightarrow{} (a = b) \mvee{} ((f b < b) \mwedge{} a \mleq{}(X;f) f b) \mvee{} ((\muparrow{}b \mmember{}\msubb{} prior(X)) \mwedge{} a \mleq{}(X;f) prior(X)(b)))
Date html generated:
2011_08_16-PM-05_54_07
Last ObjectModification:
2011_06_20-AM-01_38_03
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