{ 
[Info,A,B:Type]. [X:EClass(A)]. [b:A 
B]. [f:B A B].
(accum-class(b,a.f[b;a];a.b[a];X) 
EClass(B)) }
{ Proof }
Definitions occuring in Statement :
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t T,
function: x:A B[x],
universe: Type
Definitions :
void: Void,
proper-iseg: L1 < L2,
iseg: l1 
l2,
nat: 
,
l_exists: (
xL. P[x]),
rev_implies: P 
Q,
iff: P 
Q,
sqequal: s ~ t,
multiply: n * m,
gt: i > j,
map: map(f;as),
natural_number: $n,
sq_type: SQType(T),
filter: filter(P;l),
permutation: permutation(T;L1;L2),
list: type List,
quotient: x,y:A//B[x; y],
length: ||as||,
true: True,
cond-class: [X?Y],
eq_knd: a = b,
fpf-dom: x dom(f),
false: False,
limited-type: LimitedType,
pair: <a, b>,
prop: 
,
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p q,
band: p 
q,
bor: p 
q,
bnot: 
b,
int: 
,
unit: Unit,
bool: 
,
empty-bag: {},
implies: P Q,
union: left + right,
or: P Q,
guard: {T},
l_member: (x l),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
es-loc: loc(e),
es-E-interface: E(X),
Id: Id,
so_lambda: 
x.t[x],
es-interface-predecessors: (X)(e),
accum_list: accum_list(a,x.f[a; x];x.base[x];L),
single-bag: {x},
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: 
b,
dep-isect: Error :dep-isect,
record+: record+,
ifthenelse: if b then t else f fi ,
bag: bag(T),
top: Top,
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,
eclass-val: X(e),
in-eclass: e X,
subtype: S T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: x.A[x],
all: x:A. B[x],
axiom: Ax,
so_apply: x[s],
apply: f a,
so_apply: x[s1;s2],
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
equal: s = t,
universe: Type,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
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 :
es-interface-predecessors-nonempty,
Id_wf,
accum_list_wf,
es-E-interface_wf,
es-interface-predecessors_wf,
single-bag_wf,
bag_wf,
es-interface-top,
member_wf,
eclass_wf,
in-eclass_wf,
ifthenelse_wf,
es-E_wf,
subtype_rel_self,
es-base-E_wf,
event-ordering+_wf,
subtype_rel_wf,
event-ordering+_inc,
eclass-val_wf,
es-loc_wf,
bool_wf,
eqtt_to_assert,
assert_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
false_wf,
true_wf,
pos_length2,
permutation_wf,
subtype_base_sq,
bool_subtype_base,
assert_elim,
length_wf_nat,
pos-length,
equal-nil-sq-nil,
nat_wf,
empty-bag_wf
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[b:A {}\mrightarrow{} B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B].
(accum-class(b,a.f[b;a];a.b[a];X) \mmember{} EClass(B))
Date html generated:
2011_08_16-PM-04_36_41
Last ObjectModification:
2011_06_20-AM-00_59_17
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