{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(Top)]. [f:sys-antecedent(es;X)].
[a:E(X)].
f a 
(X;f) a }
{ Proof }
Definitions occuring in Statement :
cut-order: a (X;f) b,
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uall: [x:A]. B[x],
top: Top,
apply: f a,
universe: Type
Definitions :
es-causle: e c e',
rev_implies: P 
Q,
union: left + right,
or: P 
Q,
iff: P 
Q,
subtype: S 
T,
top: Top,
event_ordering: EO,
es-E: E,
lambda: 
x.A[x],
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[x]} ,
dep-isect: Error :dep-isect,
record+: record+,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
deq-member: deq-member(eq;x;L),
prop: 
,
apply: f a,
es-cut: Cut(X;f),
fset: FSet{T},
cut-of: cut(X;f;s),
implies: P Q,
universe: Type,
cut-order: a (X;f) b,
fset-member: a 
s,
assert: 
b,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
equal: s = t,
false: False,
void: Void,
event-ordering+: EO+(Info),
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
member: t T,
all: x:A. B[x],
function: x:A 
B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
limited-type: LimitedType,
intensional-universe: IType,
fpf: a:A fp-> B[a],
sq_type: SQType(T),
record: record(x.T[x]),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
record-select: r.x,
cand: A c B,
pair: <a, b>,
bool: 
,
eclass-val: X(e),
es-prior-interface: prior(X),
in-eclass: e 
X,
guard: {T},
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
decidable: Dec(P),
es-locl: (e <loc e'),
es-causl: (e < e'),
es-le: e loc e' ,
es-p-le: e p e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
infix_ap: x f y,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
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'),
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,
label: ...$L... t,
btrue: tt,
isl: isl(x),
can-apply: can-apply(f;x)
Lemmas :
subtype_base_sq,
bool_subtype_base,
bool_wf,
assert_elim,
es-causle_wf,
decidable__es-causle,
sq_stable_from_decidable,
es-E-interface-subtype_rel,
cut-order_weakening,
es-prior-interface_wf,
eclass-val_wf2,
es-prior-interface_wf1,
es-prior-interface_wf0,
in-eclass_wf,
es-causl_wf,
subtype_rel_wf,
subtype_rel_self,
es-base-E_wf,
decidable__equal_es-E-interface,
intensional-universe_wf,
es-interface-subtype_rel2,
cut-order_witness,
cut-order_wf,
cut-of_wf,
fset-member_wf,
assert_wf,
false_wf,
ifthenelse_wf,
deq-member_wf,
true_wf,
member_wf,
es-E-interface_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
cut-order-iff1
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[a:E(X)]. f a \mleq{}(X;f) a
Date html generated:
2011_08_16-PM-05_54_26
Last ObjectModification:
2011_06_20-AM-01_38_10
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