{ 
[Info,A:Type]. [f:A 
]. [X:EClass(A)]. [size:
]. [num:A ].
[P:A 
].
(es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v])
EClass( 
{s:i: {v:A| f[v] = i} + Top| 
isl(s)} )) }
{ Proof }
Definitions occuring in Statement :
es-collect-filter-max-aux: es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v]),
eclass: EClass(A[eo; e]),
isl: isl(x),
assert: b,
bool: ,
nat_plus: ,
nat: ,
uall: [x:A]. B[x],
top: Top,
so_apply: x[s],
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
product: x:A B[x],
union: left + right,
int: ,
universe: Type,
equal: s = t
Definitions :
pair: <a, b>,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
Knd: Knd,
tag-by: zT,
rev_implies: P 
Q,
or: P 
Q,
implies: P 
Q,
iff: P Q,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 
T2,
b-union: A 
B,
bag: bag(T),
list: type List,
true: True,
fpf-sub: f 
g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
es-E-interface: E(X),
so_lambda: 
x.t[x],
prop: 
,
fpf-cap: f(x)?z,
subtype: S T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: x.A[x],
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,
es-collect-filter-max-aux: es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v]),
apply: f a,
bool: ,
universe: Type,
function: x:A B[x],
so_lambda: x y.t[x; y],
nat_plus: ,
uall: [x:A]. B[x],
isect: x:A. B[x],
member: t T,
Auto: Error :Auto,
D: Error :D,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
Try: Error :Try,
pi2: snd(t),
isl: isl(x),
assert: b,
top: Top,
so_apply: x[s],
int: ,
equal: s = t,
set: {x:A| B[x]} ,
product: x:A B[x],
union: left + right,
nat: ,
eclass: EClass(A[eo; e]),
quotient: x,y:A//B[x; y],
natural_number: $n,
IdLnk: IdLnk,
l_member: (x l),
bfalse: ff,
Id: Id,
btrue: tt,
sq_type: SQType(T),
es-interface-predecessors: (X)(e),
eq_int: (i =
j),
mapfilter: mapfilter(f;P;L),
list_accum: list_accum(x,a.f[x; a];y;l),
so_apply: x[s1;s2],
in-eclass: e 
X,
rev_uimplies: rev_uimplies(P;Q),
squash: 
T,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
record-select: r.x,
es-collect-accum: es-collect-accum(X;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(),
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
guard: {T},
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
eclass-val: X(e),
rationals: 
,
has-value: has-value(a),
unit: Unit,
void: Void,
CollapseTHENA: Error :CollapseTHENA,
inl: inl x ,
pi1: fst(t),
lt_int: i <z j,
callbyvalue: callbyvalue,
it: 
,
inr: inr x ,
es-collect-filter-accum: es-collect-filter-accum,
AssertBY: Error :AssertBY,
band: p q,
filter: filter(P;l),
length: ||as||,
es-loc: loc(e),
alle-lt: e<e'.P[e],
es-first-at: e is first@ i s.t. e.P[e],
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
sq_stable: SqStable(P),
i-member: r I,
real: 
,
grp_car: |g|,
list-max-aux: list-max-aux(x.f[x];L),
tactic: Error :tactic,
eq_knd: a = b,
fpf-dom: x dom(f),
intensional-universe: IType,
int_eq: if a=b then c else d,
atom_eq: atomeqn def,
sqequal: s ~ t,
append: as @ bs,
locl: locl(a),
atom: Atom$n,
cand: A c B,
no_repeats: no_repeats(T;l),
prime_ideal_p: IsPrimeIdeal(R;P),
integ_dom_p: IsIntegDom(r),
grp_leq: a b,
monoid_hom_p: IsMonHom{M1,M2}(f),
group_p: IsGroup(T;op;id;inv),
monoid_p: IsMonoid(T;op;id),
monot: monot(T;x,y.R[x; y];f),
cancel: Cancel(T;S;op),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
action_p: IsAction(A;x;e;S;f),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
bilinear: BiLinear(T;pl;tm),
inverse: Inverse(T;op;id;inv),
comm: Comm(T;op),
assoc: Assoc(T;op),
ident: Ident(T;op;id),
coprime: CoPrime(a,b),
connex: Connex(T;x,y.R[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
eqfun_p: IsEqFun(T;eq),
inv_funs: InvFuns(A;B;f;g),
uni_sat: a = !x:T. Q[x],
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
es-fset-loc: i locs(s),
existse-between3: 
e(e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
alle-between2: e[e1,e2].P[e],
existse-between1: e[e1,e2).P[e],
alle-between1: e[e1,e2).P[e],
alle-le: ee'.P[e],
existse-le: ee'.P[e],
existse-before: e<e'.P[e],
es-causle: e c e',
es-le: e loc e' ,
es-locl: (e <loc e'),
es-causl: (e < e'),
cs-precondition: state s may consider v in inning i,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
cs-passed: by state s, a passed inning i without archiving a value,
cs-archived: by state s, a archived v in inning i,
cs-not-completed: in state s, a has not completed inning i,
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
p-outcome: Outcome,
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
l_disjoint: l_disjoint(T;l1;l2),
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
l_contains: A B,
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
infix_ap: x f y,
grp_lt: a < b,
set_lt: a <p b,
set_leq: a b,
assoced: a ~ b,
divides: b | a,
exists: x:A. B[x],
decidable: Dec(P),
can-apply: can-apply(f;x),
add: n + m,
spread: spread def,
map: map(f;as),
gt: i > j,
multiply: n * m,
iseg: l1 l2,
proper-iseg: L1 < L2,
limited-type: LimitedType,
nil: [],
select: l[i],
remove-repeats: remove-repeats(eq;L),
last: last(L),
hd: hd(l),
cons: [car / cdr]
Lemmas :
es-interface-predecessors-member,
eq_int_eq_true,
l_member_subtype,
l_member-settype,
l_all_wf,
list-set-type2,
sq_stable__equal,
sq_stable_wf,
property-from-l_member,
l_exists_wf,
mapfilter-not-nil,
length_wf_nat,
equal-nil-sq-nil,
not_wf,
pos-length,
list-max-aux-property,
bool_sq,
rev_implies_wf,
iff_wf,
decidable__assert,
sq_stable_from_decidable,
list-subtype,
l_member_wf,
assert-eq-id,
btrue_wf,
bfalse_wf,
intensional-universe_wf,
es-interface-val_wf2,
eq_int_wf,
es-loc_wf,
list-max-aux_wf,
sq_stable__assert,
is-collect-filter-accum,
es-E-interface_wf,
es-interface-set-subtype,
pi1_wf_top,
lt_int_wf,
int_inc,
rational-has-value,
unit_wf,
it_wf,
es-collect-filter-accum_wf,
es-interface-top,
es-base-E_wf,
subtype_rel_self,
collect-filter-accum-val,
assert_functionality_wrt_uiff,
eclass-val_wf,
squash_wf,
subtype_base_sq,
bool_subtype_base,
assert_elim,
in-eclass_wf,
es-interface-predecessors_wf,
Id_wf,
mapfilter_wf,
uiff_inversion,
top_wf,
assert_wf,
event-ordering+_wf,
es-E_wf,
nat_wf,
member_wf,
eclass_wf,
event-ordering+_inc,
nat_plus_wf,
bool_wf,
subtype_rel_wf,
es-interface-subtype_rel,
pi2_wf,
isl_wf,
subtype_rel_set,
false_wf,
ifthenelse_wf,
true_wf
\mforall{}[Info,A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbZ{}]. \mforall{}[X:EClass(A)]. \mforall{}[size:\mBbbN{}\msupplus{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}].
(es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v])
\mmember{} EClass(\mBbbN{} \mtimes{} \{s:i:\mBbbZ{} \mtimes{} \{v:A| f[v] = i\} + Top| \muparrow{}isl(s)\} ))
Date html generated:
2011_08_16-PM-05_31_22
Last ObjectModification:
2010_12_22-PM-12_32_10
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