{ 
[Info:Type]. [es:EO+(Info)]. [A:Type]. [f:A 
]. [X:EClass(A)].
[size:
]. [num:A ]. [P:A 
]. [e:E].
uiff(
e
es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v]);(e X)
e is first@ loc(e) s.t. c.||filter(
c.((num[X(c)] =
num[X(e)])
P[X(c)]);
(X)(c))||
= size
e'<e.(e' X)
((num[X(e')] num[X(e)]) ((num[X(e')] = num[X(e)]) (P[X(e')])))
(0 < ||mapfilter(c.X(c);c.(num[X(c)] = num[X(e)]);(X)(e))||)) }
{ 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]),
es-interface-predecessors: (X)(e),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: e<e'.P[e],
es-loc: loc(e),
es-E: E,
length: ||as||,
eq_int: (i = j),
band: p q,
assert: b,
bool: ,
nat_plus: ,
nat: ,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
so_apply: x[s],
le: A B,
implies: P Q,
and: P Q,
less_than: a < b,
lambda: x.A[x],
function: x:A B[x],
natural_number: $n,
int: ,
universe: Type,
equal: s = t,
mapfilter: mapfilter(f;P;L),
filter: filter(P;l)
Definitions :
infix_ap: x f y,
es-causl: (e < e'),
bfalse: ff,
unit: Unit,
int_eq: if a=b then c else d,
btrue: tt,
atom_eq: atomeqn def,
sq_type: SQType(T),
append: as @ bs,
locl: locl(a),
atom: Atom$n,
can-apply: can-apply(f;x),
intensional-universe: IType,
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]),
Knd: Knd,
IdLnk: IdLnk,
proper-iseg: L1 < L2,
iseg: l1 l2,
l_exists: (
xL. P[x]),
sqequal: s ~ t,
list: type List,
multiply: n * m,
gt: i > j,
map: map(f;as),
exists: x:A. B[x],
cand: A c B,
cond-class: [X?Y],
or: P 
Q,
guard: {T},
eq_knd: a = b,
fpf-dom: x dom(f),
natural_number: $n,
int_nzero: 
,
real: 
,
grp_car: |g|,
limited-type: LimitedType,
fpf: a:A fp-> B[a],
isl: isl(x),
l_member: (x l),
es-E-interface: E(X),
mapfilter: mapfilter(f;P;L),
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
es-collect-filter-max-aux: es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v]),
in-eclass: e X,
rev_implies: P 
Q,
iff: P Q,
so_lambda: 
x.t[x],
es-locl: (e <loc e'),
es-interface-predecessors: (X)(e),
eclass-val: X(e),
so_apply: x[s],
eq_int: (i = j),
band: p q,
filter: filter(P;l),
length: ||as||,
axiom: Ax,
es-loc: loc(e),
Id: Id,
prop: 
,
pair: <a, b>,
less_than: a < b,
le: A B,
not: 
A,
implies: P Q,
alle-lt: e<e'.P[e],
es-first-at: e is first@ i s.t. e.P[e],
void: Void,
false: False,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
bool: ,
set: {x:A| B[x]} ,
nat: ,
union: left + right,
nat_plus: ,
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
int: ,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
member: t T,
event-ordering+: EO+(Info),
equal: s = t,
tactic: Error :tactic,
fpf-cap: f(x)?z,
quotient: x,y:A//B[x; y],
rationals: 
,
has-value: has-value(a),
inl: inl x ,
pi1: fst(t),
lt_int: i <z j,
callbyvalue: callbyvalue,
it: 
,
inr: inr x ,
so_apply: x[s1;s2],
es-collect-filter-accum: es-collect-filter-accum,
fpf-sub: f g,
map-class: (f[v] where v from X),
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
nil: [],
add: n + m
Lemmas :
filter-filter,
filter_wf_top,
subtype_rel_list,
subtype_rel_set,
filter-le,
length-map,
iff_functionality_wrt_iff,
is-collect-filter-accum,
es-collect-filter-accum_wf,
it_wf,
rational-has-value,
int_inc,
lt_int_wf,
pi1_wf_top,
es-interface-subtype_rel,
assert_wf,
true_wf,
in-eclass_wf,
ifthenelse_wf,
false_wf,
es-first-at_wf,
alle-lt_wf,
le_wf,
assert_witness,
uiff_wf,
es-locl_wf,
es-E_wf,
event-ordering+_inc,
subtype_rel_self,
bool_wf,
nat_wf,
nat_plus_wf,
event-ordering+_wf,
eclass_wf,
not_wf,
Id_wf,
length_wf_nat,
eclass-val_wf,
es-interface-predecessors_wf,
es-E-interface_wf,
mapfilter_wf,
pos_length2,
es-collect-filter-max-aux_wf,
member_wf,
subtype_rel_wf,
top_wf,
es-interface-top,
es-loc_wf,
filter_wf,
length_wf1,
band_wf,
eq_int_wf,
rev_implies_wf,
iff_wf,
pos-length,
equal-nil-sq-nil,
es-interface-subtype_rel2,
isl_wf,
intensional-universe_wf,
list-subtype,
l_member_wf,
filter_type,
iff_weakening_uiff,
uiff_inversion,
assert-eq-id,
subtype_base_sq,
bool_subtype_base,
assert_elim,
nat_plus_properties,
btrue_wf,
bfalse_wf,
unit_wf,
es-interface-val_wf2
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[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{}]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v]);(\muparrow{}e \mmember{}\msubb{} X)
\mwedge{} e is first@ loc(e) s.t. c.||filter(\mlambda{}c.((num[X(c)] =\msubz{} num[X(e)]) \mwedge{}\msubb{} P[X(c)]);\mleq{}(X)(c))|| = size
\mwedge{} \mforall{}e'<e.(\muparrow{}e' \mmember{}\msubb{} X) {}\mRightarrow{} ((num[X(e')] \mleq{} num[X(e)]) \mwedge{} ((num[X(e')] = num[X(e)]) {}\mRightarrow{} (\muparrow{}P[X(e')])))
\mwedge{} (0 < ||mapfilter(\mlambda{}c.X(c);\mlambda{}c.(num[X(c)] =\msubz{} num[X(e)]);\mleq{}(X)(e))||))
Date html generated:
2011_08_16-PM-05_31_42
Last ObjectModification:
2011_06_20-AM-01_25_04
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