{ 
[Info,A:Type].
Xs:EClass(A) List. es:EO+(Info). e:E.
(
e 
first-eclass(Xs) 
(
XXs. e X)) }
{ Proof }
Definitions occuring in Statement :
first-eclass: first-eclass(Xs),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
list: type List,
universe: Type,
l_exists: (xL. P[x])
Definitions :
last: last(L),
append: as @ bs,
fpf: a:A fp-> B[a],
cons: [car / cdr],
first-eclass: first-eclass(Xs),
in-eclass: e X,
minus: -n,
add: n + m,
strong-subtype: strong-subtype(A;B),
real: 
,
int_iseg: {i...j},
rev_implies: P Q,
natural_number: $n,
subtract: n - m,
firstn: firstn(n;as),
bfalse: ff,
eq_atom: eq_atom$n(x;y),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
eq_atom: x =a y,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
btrue: tt,
sq_type: SQType(T),
bool: 
,
subtype_rel: A 
r B,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
bnot: 
b,
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
set_car: |p|,
grp_car: |g|,
rng_car: |r|,
limited-type: LimitedType,
atom: Atom$n,
rationals: 
,
Id: Id,
IdLnk: IdLnk,
nil: [],
nequal: a 
b T ,
ge: i 
j ,
not: A,
sqequal: s ~ t,
false: False,
null: null(as),
union: left + right,
or: P 
Q,
divides: b | a,
assoced: a ~ b,
set_leq: a 
b,
set_lt: a <p b,
grp_lt: a < b,
cand: A c
B,
l_member: (x l),
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
set: {x:A| B[x]} ,
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
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' ,
es-causle: e c 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),
apply: f a,
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
void: Void,
top: Top,
int: 
,
uimplies: b supposing a,
less_than: a < b,
length: ||as||,
nat: 
,
le: A B,
prop: 
,
guard: {T},
subtype: S T,
lambda: 
x.A[x],
equal: s = t,
member: t T,
quotient: x,y:A//B[x; y],
bag: bag(T),
exists: x:A. B[x],
implies: P Q,
product: x:A 
B[x],
and: P Q,
list: type List,
universe: Type,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
all: x:A. B[x],
function: x:A 
B[x],
iff: P Q,
l_exists: (xL. P[x]),
so_lambda: 
x.t[x],
eclass: EClass(A[eo; e]),
so_lambda: x y.t[x; y],
assert: b,
es-E: E,
event-ordering+: EO+(Info),
event_ordering: EO,
axiom: Ax,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
eq_int: (i =
j),
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
MaAuto: Error :MaAuto,
ParallelOp: Error :ParallelOp,
RepeatFor: Error :RepeatFor,
tl: tl(l),
hd: hd(l),
empty-bag: {},
bag-size: bag-size(bs),
list_accum: list_accum(x,a.f[x; a];y;l),
RepUR: Error :RepUR,
so_apply: x[s],
locl: locl(a),
Knd: Knd,
pair: <a, b>,
lt_int: i <z j,
le_int: i z 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),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
band: p q,
bor: p q,
unit: Unit
Lemmas :
eq_int_eq_true,
assert_witness,
assert_of_eq_int,
eqff_to_assert,
eqtt_to_assert,
assert_elim,
iff_weakening_uiff,
or_functionality_wrt_uiff3,
or_functionality_wrt_uiff2,
decidable_wf,
decidable__false,
list_accum_wf,
empty-bag_wf,
eq_int_wf,
bag-size_wf,
bag_wf,
list_accum_append,
or_functionality_wrt_iff,
l_exists_cons,
iff_transitivity,
l_exists_append,
append_wf,
last_wf,
null_wf,
ge_wf,
nat_properties,
nat_ind_tp,
l_exists_wf,
eclass_wf,
assert_wf,
le_wf,
guard_wf,
event-ordering+_wf,
es-E_wf,
iff_wf,
comp_nat_ind_tp,
nat_wf,
event-ordering+_inc,
uall_wf,
length_wf1,
length_wf_nat,
top_wf,
member_wf,
decidable__assert,
null_wf3,
last-lemma-sq,
pos_length,
not_wf,
uiff_transitivity,
not_functionality_wrt_uiff,
uiff_wf,
assert_of_null,
assert_of_bnot,
bnot_wf,
false_wf,
ifthenelse_wf,
true_wf,
bool_wf,
subtype_base_sq,
bool_subtype_base,
not_assert_elim,
es-base-E_wf,
subtype_rel_self,
btrue_wf,
firstn_wf,
rev_implies_wf,
length_firstn,
int_iseg_wf,
all_functionality_wrt_iff,
iff_functionality_wrt_iff,
l_exists_nil,
in-eclass_wf,
first-eclass_wf,
l_member_wf,
subtype_rel_wf,
es-interface-top
\mforall{}[Info,A:Type].
\mforall{}Xs:EClass(A) List. \mforall{}es:EO+(Info). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} first-eclass(Xs) \mLeftarrow{}{}\mRightarrow{} (\mexists{}X\mmember{}Xs. \muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2011_08_16-PM-04_18_42
Last ObjectModification:
2011_06_20-AM-00_46_08
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