{ 
[Info,A,B:Type]. [X:EClass(A)]. [P:B 
]. [num:A 
]. [init:B].
[f:B A B].
(es-collect-accum(X;x.num[x];init;b,v.f[b;v];b.P[b]) 
EClass( 
B)) }
{ Proof }
Definitions occuring in Statement :
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
eclass: EClass(A[eo; e]),
bool: ,
nat: ,
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t T,
function: x:A B[x],
product: x:A B[x],
universe: Type
Definitions :
bfalse: ff,
decide_bfalse: decide_bfalse{decide_bfalse_compseq_tag_def:o}(v11.g[v11]; v21.f[v21]),
ifthenelse: if b then t else f fi ,
sum-map: 
f[x] for x L,
sum: (f[x] | x < k),
imax: imax(a;b),
length: ||as||,
multiply: n * m,
filter: filter(P;l),
es-E-interface: E(X),
sq_type: SQType(T),
add: n + m,
real: 
,
rationals: 
,
inl: inl x ,
spread: spread def,
sq_stable: SqStable(P),
or: P 
Q,
guard: {T},
eq_knd: a = b,
fpf-dom: x dom(f),
permutation: permutation(T;L1;L2),
list: type List,
quotient: x,y:A//B[x; y],
empty-bag: {},
subtract: n - m,
single-bag: {x},
decide: case b of inl(x) => s[x] | inr(y) => t[y],
spreadn: spread3,
false: False,
bag: bag(T),
void: Void,
l_member: (x l),
so_lambda: 
x.t[x],
prop: 
,
pi1: fst(t),
pi2: snd(t),
isl: isl(x),
assert: 
b,
implies: P 
Q,
union: left + right,
int: 
,
set: {x:A| B[x]} ,
inr: inr x ,
natural_number: $n,
minus: -n,
pair: <a, b>,
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
es-interface-accum: es-interface-accum(f;x;X),
collect_filter: collect_filter(),
es-filter-image: f[X],
subtype: S 
T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: x.A[x],
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,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
axiom: Ax,
so_apply: x[s1;s2],
apply: f a,
so_apply: x[s],
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
product: x:A B[x],
nat: ,
equal: s = t,
universe: Type,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
bool: ,
function: x:A B[x],
member: t T,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
exists: 
x:A. B[x],
true: True,
MaAuto: Error :MaAuto,
D: Error :D,
CollapseTHEN: Error :CollapseTHEN
Lemmas :
ifthenelse_wf,
true_wf,
subtype_base_sq,
union_subtype_base,
isect_subtype_base,
top_wf,
member_wf,
pi1_wf_top,
le_wf,
es-interface-accum_wf,
assert_wf,
nat_wf,
pi2_wf,
isl_wf,
es-filter-image_wf,
collect_accum-wf2,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
eclass_wf,
bool_wf,
bag_wf,
permutation_wf,
single-bag_wf,
not_wf,
false_wf,
subtype_rel_wf,
empty-bag_wf,
bfalse_wf
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:B {}\mrightarrow{} \mBbbB{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[init:B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B].
(es-collect-accum(X;x.num[x];init;b,v.f[b;v];b.P[b]) \mmember{} EClass(\mBbbN{} \mtimes{} B))
Date html generated:
2011_08_16-PM-05_27_12
Last ObjectModification:
2011_06_20-AM-01_23_51
Home
Index