{ 
[Info,T:Type]. [G:es:EO+(Info) 
E bag(T)]. [F:es:EO+(Info)
e':E
T
{e:E| (e' <loc e)}
bag(T)].
(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]) 
EClass(T)) }
{ Proof }
Definitions occuring in Statement :
es-rec-class: es-rec-class,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uall: [x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
universe: Type,
bag: bag(T)
Definitions :
es-local-pred: last(P),
let: let,
local-pred-class: local-pred-class(P),
eclass-val: X(e),
true: True,
squash: 
T,
es-causl: (e < e'),
limited-type: LimitedType,
real: 
,
grp_car: |g|,
minus: -n,
add: n + m,
subtract: n - m,
false: False,
natural_number: $n,
int: 
,
nat: 
,
implies: P 
Q,
exists: 
x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
es-E-interface: E(X),
es-prior-interface: prior(X),
in-eclass: e 
X,
record-select: r.x,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: 
b,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
record+: record+,
void: Void,
lambda: 
x.A[x],
ycomb: Y,
prop: 
,
subtype: S 
T,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
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,
all: x:A. B[x],
so_lambda: 
x y.t[x; y],
axiom: Ax,
so_apply: x[s1;s2;s3;s4],
apply: f a,
so_apply: x[s1;s2],
es-rec-class: es-rec-class,
eclass: EClass(A[eo; e]),
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
bag: bag(T),
set: {x:A| B[x]} ,
es-locl: (e <loc e'),
event-ordering+: EO+(Info),
es-E: E,
event_ordering: EO,
top: Top,
function: x:A B[x],
intensional-universe: IType,
cand: A c B,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
es-loc: loc(e),
so_apply: x[s],
l_member: (x l),
inr: inr x ,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
pair: <a, b>,
guard: {T},
sq_type: SQType(T),
Id: Id,
inl: inl x ,
bag-only: only(bs),
bag_only_single: bag_only_single{bag_only_single_compseq_tag_def:o}(x),
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
infix_ap: x f y,
bool: 
,
bag-size: bag-size(bs),
eq_int: (i =
j),
or: P 
Q,
union: left + right,
sq_exists: x:{A| B[x]},
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
Try: Error :Try,
Complete: Error :Complete,
D: Error :D,
THENM: Error :THENM,
CollapseTHENA: Error :CollapseTHENA,
quotient: x,y:A//B[x; y],
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_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
Lemmas :
assert_of_eq_int,
assert_wf,
not_wf,
eq_int_wf,
bag-size_wf,
subtype_rel_wf,
es-local-pred_wf,
bool_wf,
bag-only_wf,
Id_wf,
es-local-pred_wf2,
es-base-E_wf,
subtype_rel_self,
intensional-universe_wf,
false_wf,
es-E_wf,
bag_wf,
member_wf,
top_wf,
event-ordering+_wf,
event-ordering+_inc,
es-locl_wf,
eclass_wf,
ifthenelse_wf,
in-eclass_wf,
es-causl-swellfnd,
nat_wf,
nat_properties,
ge_wf,
le_wf,
es-causl_wf
\mforall{}[Info,T:Type]. \mforall{}[G:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} bag(T)]. \mforall{}[F:es:EO+(Info)
{}\mrightarrow{} e':E
{}\mrightarrow{} T
{}\mrightarrow{} \{e:E| (e' <loc e)\}
{}\mrightarrow{} bag(T)].
(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]) \mmember{} EClass(T))
Date html generated:
2011_08_16-PM-05_02_36
Last ObjectModification:
2011_06_20-AM-01_09_12
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