{ 
[Info:Type]
es:EO+(Info)
[A:Type]
X:EClass(A)
[S:Type]
init:S. f:S 
A S. test:S A 
. nxt:S 
A S. e:E.
(
e 
Threshold(init;f;test;nxt;X)
(e X)
let v = X(e) in
let s = if e prior(Threshold(init;f;test;nxt;X))
then let e' = prior(Threshold(init;f;test;
nxt;X))(e) in
list_accum(s,v.f s v;
nxt
Threshold(init;f;test;
nxt;X)(e');
X(e', e))
else list_accum(s,v.f s v;init;X(<e))
fi in
(test s v)) }
{ Proof }
Definitions occuring in Statement :
es-threshold: Threshold(init;f;test;nxt;X),
es-prior-interface: prior(X),
es-prior-interval-vals: X(e1, e2),
es-prior-interface-vals: X(<e),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
ifthenelse: if b then t else f fi ,
bool: ,
let: let,
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
and: P Q,
apply: f a,
function: x:A B[x],
product: x:A B[x],
universe: Type,
list_accum: list_accum(x,a.f[x; a];y;l)
Definitions :
cand: A c B,
Knd: Knd,
IdLnk: IdLnk,
rationals: 
,
sq_type: SQType(T),
es-local-pred: last(P),
es-rec-class: es-rec-class,
fpf-cap: f(x)?z,
filter: filter(P;l),
list: type List,
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
set_eq: =,
set_le: 
,
grp_eq: =,
rng_eq: =,
real: 
,
grp_car: |g|,
nat: 
,
quotient: x,y:A//B[x; y],
axiom: Ax,
rev_implies: P Q,
natural_number: $n,
bag-size: bag-size(bs),
es-prior-interface: prior(X),
es-threshold: Threshold(init;f;test;nxt;X),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
less_than: a < b,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
es-loc: loc(e),
Id: Id,
es-causl: (e < e'),
es-locl: (e <loc e'),
cond-class: [X?Y],
eq_knd: a = b,
fpf-dom: x dom(f),
limited-type: LimitedType,
prop: 
,
bfalse: ff,
btrue: tt,
uiff: uiff(P;Q),
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
set_blt: a < b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
not: 
A,
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
band: p q,
bor: p 
q,
bnot: b,
int: 
,
unit: Unit,
so_apply: x[s],
union: left + right,
or: P Q,
guard: {T},
l_member: (x l),
subtype_rel: A 
r B,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
es-E-interface: E(X),
uimplies: b supposing a,
top: Top,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
bag: bag(T),
set: {x:A| B[x]} ,
record-select: r.x,
lambda: 
x.A[x],
subtype: S T,
event_ordering: EO,
es-E: E,
bool: ,
event-ordering+: EO+(Info),
iff: P Q,
implies: P Q,
and: P Q,
assert: b,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
true: True,
member: t T,
equal: s = t,
false: False,
void: Void,
universe: Type,
all: x:A. B[x],
function: x:A B[x],
eclass: EClass(A[eo; e]),
isect: 
x:A. B[x],
uall: [x:A]. B[x],
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try,
RepeatFor: Error :RepeatFor,
in-eclass: e X,
Auto: Error :Auto,
empty-bag: {},
pair: <a, b>,
single-bag: {x},
apply: f a,
ifthenelse: if b then t else f fi ,
es-prior-interval-vals: X(e1, e2),
list_accum: list_accum(x,a.f[x; a];y;l),
let: let,
eclass-val: X(e),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
es-prior-interface-vals: X(<e),
so_lambda: 
x y.t[x; y],
product: x:A B[x]
Lemmas :
bag_wf,
es-interface-top,
member_wf,
eclass_wf,
in-eclass_wf,
ifthenelse_wf,
es-E_wf,
assert_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
eclass-val_wf,
es-prior-interface-vals_wf,
list_accum_wf,
empty-bag_wf,
single-bag_wf,
is-rec-class,
bool_wf,
eqtt_to_assert,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
es-locl_wf,
es-prior-interval-vals_wf,
subtype_rel_wf,
iff_wf,
true_wf,
assert_witness,
false_wf,
es-threshold_wf,
es-prior-interface_wf1,
bag-size_wf,
nat_wf,
es-prior-interface_wf,
es-interface-subtype_rel2,
top_wf,
es-E-interface_wf,
list-subtype,
l_member_wf,
eclass-val_wf2,
es-interface-val_wf2,
es-interface-val_wf,
assert_elim,
subtype_base_sq,
bool_subtype_base,
rev_implies_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A:Type]
\mforall{}X:EClass(A)
\mforall{}[S:Type]
\mforall{}init:S. \mforall{}f:S {}\mrightarrow{} A {}\mrightarrow{} S. \mforall{}test:S {}\mrightarrow{} A {}\mrightarrow{} \mBbbB{}. \mforall{}nxt:S \mtimes{} A {}\mrightarrow{} S. \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} Threshold(init;f;test;nxt;X)
\mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} X)
\mwedge{} let v = X(e) in
let s = if e \mmember{}\msubb{} prior(Threshold(init;f;test;nxt;X))
then let e' = prior(Threshold(init;f;test;nxt;X))(e) in
list\_accum(s,v.f s v;
nxt Threshold(init;f;test;nxt;X)(e');
X(e', e))
else list\_accum(s,v.f s v;init;X(<e))
fi in
\muparrow{}(test s v))
Date html generated:
2011_08_16-PM-05_11_11
Last ObjectModification:
2011_06_20-AM-01_13_23
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