{ 
[Info,A:Type]. [X:EClass(A)]. [S:Type]. [init:S]. [f:S 
A S].
[test:S A 
]. [nxt:S 
A S].
(Threshold(init;f;test;nxt;X) 
EClass(S A)) }
{ Proof }
Definitions occuring in Statement :
es-threshold: Threshold(init;f;test;nxt;X),
eclass: EClass(A[eo; e]),
bool: ,
uall: [x:A]. B[x],
member: t T,
function: x:A B[x],
product: x:A B[x],
universe: Type
Definitions :
Id: Id,
void: Void,
cond-class: [X?Y],
so_apply: x[s],
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
limited-type: LimitedType,
bfalse: ff,
btrue: tt,
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,
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,
bnot: 
b,
int: 
,
unit: Unit,
es-prior-interface: prior(X),
exists: x:A. B[x],
es-interface-at: X@i,
intensional-universe: IType,
tag-by: zT,
rev_implies: P 
Q,
or: P Q,
iff: P Q,
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 
T2,
b-union: A 
B,
fpf-cap: f(x)?z,
union: left + right,
record: record(x.T[x]),
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,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f 
g,
squash: 
T,
sq_stable: SqStable(P),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
true: True,
false: False,
implies: P Q,
es-E-interface: E(X),
permutation: permutation(T;L1;L2),
list: type List,
quotient: x,y:A//B[x; y],
so_lambda: 
x.t[x],
infix_ap: x f y,
es-causl: (e < e'),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: 
b,
le: A B,
ge: i 
j ,
not: A,
less_than: a < b,
uimplies: b supposing a,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
prop: 
,
subtype: S T,
dep-isect: Error :dep-isect,
record+: record+,
top: Top,
bag: bag(T),
es-locl: (e <loc e'),
set: {x:A| B[x]} ,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
all: x:A. B[x],
axiom: Ax,
es-prior-interval-vals: X(e1, e2),
eclass-val: X(e),
es-prior-interface-vals: X(<e),
list_accum: list_accum(x,a.f[x; a];y;l),
empty-bag: {},
pair: <a, b>,
single-bag: {x},
lambda: x.A[x],
apply: f a,
let: let,
in-eclass: e X,
ifthenelse: if b then t else f fi ,
es-rec-class: es-rec-class,
product: x:A B[x],
bool: ,
es-threshold: Threshold(init;f;test;nxt;X),
equal: s = t,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
universe: Type,
uall: [x:A]. B[x],
isect: x:A. B[x],
member: t T,
function: x:A B[x],
MaAuto: Error :MaAuto,
Unfold: Error :Unfold,
CollapseTHEN: Error :CollapseTHEN
Lemmas :
ifthenelse_wf,
bag_wf,
single-bag_wf,
eclass-val_wf,
list_accum_wf,
es-prior-interface-vals_wf,
member_wf,
es-interface-top,
subtype_rel_wf,
eclass_wf,
es-locl_wf,
es-prior-interval-vals_wf,
in-eclass_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
empty-bag_wf,
es-rec-class_wf,
bool_wf,
uall_wf,
permutation_wf,
assert_wf,
false_wf,
true_wf,
es-base-E_wf,
subtype_rel_self,
es-interface-val_wf2,
es-E-interface_wf,
es-interface-val_wf,
sq_stable__assert,
intensional-universe_wf,
eqtt_to_assert,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf
\mforall{}[Info,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].
(Threshold(init;f;test;nxt;X) \mmember{} EClass(S \mtimes{} A))
Date html generated:
2011_08_16-PM-05_10_53
Last ObjectModification:
2011_06_20-AM-01_13_15
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