{ 
[Info,A1:Type]. [n:
]. [X:EClass(A1)].
(Buffer(n;X)
= es-interface-accum(
L,v.if ||L|| <z n then L @ [v] else tl(L @ [v]) fi ;
[];X)) }
{ Proof }
Definitions occuring in Statement :
es-interface-buffer: Buffer(n;X),
es-interface-accum: es-interface-accum(f;x;X),
eclass: EClass(A[eo; e]),
tl: tl(l),
length: ||as||,
append: as @ bs,
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
nat: ,
uall: [x:A]. B[x],
lambda: x.A[x],
cons: [car / cdr],
nil: [],
list: type List,
universe: Type,
equal: s = t
Definitions :
assert: 
b,
bag: bag(T),
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
implies: P 
Q,
false: False,
not: 
A,
le: A 
B,
int: 
,
axiom: Ax,
tl: tl(l),
nil: [],
cons: [car / cdr],
append: as @ bs,
length: ||as||,
lt_int: i <z j,
es-interface-accum: es-interface-accum(f;x;X),
es-interface-buffer: Buffer(n;X),
list: type List,
subtype: S 
T,
subtype_rel: A r B,
eq_atom: eq_atom$n(x;y),
atom: Atom,
apply: f a,
top: Top,
es-base-E: es-base-E(es),
token: "$token",
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: x.A[x],
isect: 
x:A. B[x],
function: x:A 
B[x],
all: x:A. B[x],
set: {x:A| B[x]} ,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
uall: [x:A]. B[x],
nat: ,
member: t 
T,
equal: s = t,
universe: Type,
tactic: Error :tactic,
sq_type: SQType(T),
es-loc: loc(e),
Id: Id,
es-interface-predecessors: (X)(e),
list_accum: list_accum(x,a.f[x; a];y;l),
cond-class: [X?Y],
so_apply: x[s],
eq_knd: a = b,
fpf-dom: x dom(f),
es-prior-interface: prior(X),
exists: 
x:A. B[x],
es-interface-at: X@i,
so_lambda: x.t[x],
tag-by: zT,
or: P 
Q,
fset: FSet{T},
dataflow: dataflow(A;B),
isect2: T1 T2,
b-union: A 
B,
fpf-cap: f(x)?z,
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),
filter: filter(P;l),
l_member: (x l),
intensional-universe: IType,
guard: {T},
eclass-val: X(e),
es-E-interface: E(X),
sqequal: s ~ t,
true: True,
rev_implies: P 
Q,
iff: P Q,
natural_number: $n,
void: Void,
bag_size_empty: bag_size_empty{bag_size_empty_compseq_tag_def:o},
bag_size_single: bag_size_single{bag_size_single_compseq_tag_def:o}(x),
limited-type: LimitedType,
prop: 
,
bfalse: ff,
btrue: tt,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
eq_bool: p =b q,
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,
in-eclass: e X,
bnot: b,
unit: Unit,
union: left + right,
bool: 
,
sv-class: Singlevalued(X),
real: 
,
grp_car: |g|,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
Complete: Error :Complete,
CollapseTHENM: Error :CollapseTHENM,
Try: Error :Try,
D: Error :D,
RepeatFor: Error :RepeatFor,
lastn: lastn(n;L),
eclass-vals: X(L),
map: map(f;as),
hd: hd(l)
Lemmas :
map_wf,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
le_int_wf,
lastn-as-accum,
eclass-vals_wf,
es-interface-extensionality,
lt_int_wf,
length_wf1,
sv-class_wf,
le_wf,
bool_wf,
eqtt_to_assert,
assert_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
in-eclass_wf,
member_wf,
subtype_rel_wf,
es-interface-top,
false_wf,
true_wf,
top_wf,
length_wf_nat,
iff_wf,
is-interface-accum,
iff_functionality_wrt_iff,
iff_weakening_uiff,
is-interface-buffer,
rev_implies_wf,
es-interface-subtype_rel2,
eclass-val_wf,
implies_functionality_wrt_iff,
intensional-universe_wf,
list-subtype,
l_member_wf,
es-interface-val_wf2,
es-E-interface_wf,
es-interface-val_wf,
sq_stable__assert,
interface-buffer-val,
es-interface-accum-val,
es-interface-predecessors_wf,
Id_wf,
list_accum_wf,
es-loc_wf,
nat_properties,
subtype_base_sq,
bool_subtype_base,
assert_elim,
nat_wf,
es-E_wf,
es-base-E_wf,
subtype_rel_self,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
es-interface-buffer_wf,
append_wf,
tl_wf,
ifthenelse_wf,
es-interface-accum_wf
\mforall{}[Info,A1:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[X:EClass(A1)].
(Buffer(n;X) = es-interface-accum(\mlambda{}L,v.if ||L|| <z n then L @ [v] else tl(L @ [v]) fi ;[];X))
Date html generated:
2011_08_16-PM-06_08_14
Last ObjectModification:
2011_06_20-AM-01_48_28
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