{ 
[Info,T:Type].
X:EClass(T). es:EO+(Info). e:E.
(
e'<e.((
v:T. v 
X(e')) 
e''<e.(v:T. v X(e'')) 
e'' 
loc e' )
(class-pred(X;es;e) = (inl e' ))
(e'<e.v:T. (
v X(e')) (class-pred(X;es;e) = (inr 
)))) }
{ Proof }
Definitions occuring in Statement :
class-pred: class-pred(X;es;e),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
alle-lt: e<e'.P[e],
existse-before: e<e'.P[e],
es-le: e loc e' ,
es-E: E,
it: ,
uall: [x:A]. B[x],
top: Top,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
squash: T,
implies: P Q,
or: P Q,
and: P Q,
inr: inr x ,
inl: inl x ,
union: left + right,
universe: Type,
equal: s = t
Definitions :
bag-size: bag-size(bs),
natural_number: $n,
less_than: a < b,
bag-member: bag-member(T;x;bs),
exists: x:A. B[x],
squash: T,
iff: P 
Q,
bag: bag(T),
uall: [x:A]. B[x],
universe: Type,
tactic: Error :tactic,
limited-type: LimitedType,
l_member: (x l),
length: ||as||,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: A,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
so_lambda: 
x.t[x],
real: 
,
grp_car: |g|,
subtype: S T,
int: 
,
nat: 
,
prop: 
,
permutation: permutation(T;L1;L2),
list: type List,
and: P Q,
product: x:A 
B[x],
rev_implies: P Q,
implies: P Q,
set: {x:A| B[x]} ,
quotient: x,y:A//B[x; y],
all: x:A. B[x],
function: x:A 
B[x],
isect: 
x:A. B[x],
equal: s = t,
member: t T,
Auto: Error :Auto,
RepUR: Error :RepUR,
CollapseTHEN: Error :CollapseTHEN,
Complete: Error :Complete,
Try: Error :Try,
D: Error :D,
axiom: Ax,
lambda: x.A[x],
pair: <a, b>,
CollapseTHENA: Error :CollapseTHENA,
apply: f a,
so_apply: x[s],
union: left + right,
or: P Q,
false: False,
void: Void,
top: Top,
cons: [car / cdr],
nil: [],
guard: {T},
sq_type: SQType(T),
null: null(as),
assert: 
b,
true: True,
RepeatFor: Error :RepeatFor,
es-causle: e c e',
tl: tl(l),
hd: hd(l),
cand: A c B,
add: n + m,
unit: Unit,
es-loc: loc(e),
Id: Id,
infix_ap: x f y,
es-causl: (e < e'),
bool: 
,
lt_int: i <z j,
es-locl: (e <loc e'),
sq_exists: x:{A| B[x]},
es-local-pred: last(P),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
dep-isect: Error :dep-isect,
record+: record+,
event_ordering: EO,
so_lambda: x y.t[x; y],
event-ordering+: EO+(Info),
existse-before: e<e'.P[e],
es-le: e loc e' ,
inl: inl x ,
alle-lt: e<e'.P[e],
classrel: v X(e),
es-E: E,
class-pred: class-pred(X;es;e),
inr: inr x ,
it: ,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
eclass-val: X(e),
es-pred: pred(e),
existse-le: ee'.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'),
decidable: Dec(P),
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),
valueall-type: valueall-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,
fpf-sub: f g,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
sq_stable: SqStable(P),
partitions: partitions(I;p),
le_int: i z j,
eq_int: (i =
j),
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),
name_eq: name_eq(x;y),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bnot: b,
bimplies: p q,
band: p q,
bor: p q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas :
sq_stable__assert,
true_wf,
ifthenelse_wf,
es-le-not-locl,
decidable__es-le,
false_wf,
assert_of_lt_int,
sq_stable_from_decidable,
decidable__es-locl,
es-causl_wf,
es-base-E_wf,
subtype_rel_self,
es-E_wf,
es-locl_wf,
assert_wf,
not_wf,
event-ordering+_wf,
lt_int_wf,
es-local-pred_wf,
event-ordering+_inc,
eclass_wf,
existse-before_wf,
classrel_wf,
alle-lt_wf,
es-le_wf,
bool_wf,
Id_wf,
es-loc_wf,
it_wf,
unit_wf,
equal-top,
cons_member,
permutation-length,
member_null,
subtype_base_sq,
int_subtype_base,
length_cons,
non_neg_length,
length_wf_nat,
top_wf,
nil_member,
squash_wf,
bag-member_wf,
member_wf,
bag-size_wf,
subtype_rel_wf,
nat_wf,
rev_implies_wf,
bag_qinc,
pair_wf,
iff_wf,
permutation_wf,
bag_wf,
l_member_wf,
length_wf1,
pos_length2
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mexists{}e'<e.((\mdownarrow{}\mexists{}v:T. v \mmember{} X(e')) \mwedge{} \mforall{}e''<e.(\mdownarrow{}\mexists{}v:T. v \mmember{} X(e'')) {}\mRightarrow{} e'' \mleq{}loc e' )
\mwedge{} (class-pred(X;es;e) = (inl e' ))
\mvee{} (\mforall{}e'<e.\mforall{}v:T. (\mneg{}v \mmember{} X(e')) \mwedge{} (class-pred(X;es;e) = (inr \mcdot{} ))))
Date html generated:
2011_08_16-PM-04_40_46
Last ObjectModification:
2011_06_15-PM-05_28_05
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