{ 
[Info,A,B:Type]. [g:B 
A]. [h:A B].
([f:A 
]. [X:EClass(B)]. [size:
]. [num:A ]. [P:A 
].
((<fst(tr)
, fst(snd(tr))
, h[snd(snd(tr))]> where tr from ...)
= Collect(size x's from X with maximum num[g[x]] such that P[g[x]]
return <num[g[x]],n,x> with n = maximum f[g[x]]))) supposing
((b:B. (h[g[b]] = b)) and
(a:A. (g[h[a]] = a))) }
{ Proof }
Definitions occuring in Statement :
es-collect-filter-max: es-collect-filter-max,
map-class: (f[v] where v from X),
eclass: EClass(A[eo; e]),
bool: ,
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
all: x:A. B[x],
set: {x:A| B[x]} ,
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
int: ,
universe: Type,
equal: s = t
Definitions :
eclass-val: X(e),
l_member: (x 
l),
record-select: r.x,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
dep-isect: Error :dep-isect,
record+: record+,
true: True,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
rev_implies: P 
Q,
in-eclass: e 
X,
assert: 
b,
implies: P 
Q,
iff: P Q,
void: Void,
limited-type: LimitedType,
subtype: S 
T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: 
x.A[x],
top: Top,
so_lambda: 
x.t[x],
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
axiom: Ax,
es-collect-filter-max: es-collect-filter-max,
pi2: snd(t),
pi1: fst(t),
pair: <a, b>,
map-class: (f[v] where v from X),
apply: f a,
so_apply: x[s],
set: {x:A| B[x]} ,
product: x:A B[x],
bool: ,
nat: ,
nat_plus: ,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
int: ,
prop: 
,
all: x:A. B[x],
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
function: x:A B[x],
uimplies: b supposing a,
isect: 
x:A. B[x],
member: t T,
Auto: Error :Auto,
Complete: Error :Complete,
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic,
sqequal: s ~ t,
union: left + right,
es-E-interface: E(X),
atom: Atom,
token: "$token",
it: 
,
int_eq: if a=b then c else d,
unit: Unit,
bfalse: ff,
b-union: A 
B,
fset: FSet{T},
isect2: T1 T2,
record: record(x.T[x]),
tag-by: zT,
cons: [car / cdr],
es-interface-at: X@i,
map: map(f;as),
nil: [],
class-program: ClassProgram(T),
fpf-dom: x dom(f),
ma-state: State(ds),
deq: EqDecider(T),
atom: Atom$n,
Knd: Knd,
locl: locl(a),
append: as @ bs,
atom_eq: atomeqn def,
or: P 
Q,
intensional-universe: IType,
natural_number: $n,
mapfilter: mapfilter(f;P;L),
band: p q,
can-apply: can-apply(f;x),
isl: isl(x),
filter: filter(P;l),
list: type List,
es-interface-predecessors: (X)(e),
btrue: tt,
eq_int: (i =
j),
grp_car: |g|,
real: 
,
fpf-sub: f g,
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
rnonneg: rnonneg(r),
req: x = y,
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
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],
sq_stable: SqStable(P),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
same-thread: same-thread(es;p;e;e'),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';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,
cand: A c B,
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),
squash: 
T,
Id: Id,
es-loc: loc(e),
length: ||as||,
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: e<e'.P[e],
sq_type: SQType(T),
guard: {T},
fpf-cap: f(x)?z,
es-base-E: es-base-E(es),
cond-class: [X?Y],
eq_knd: a = b,
MaAuto: Error :MaAuto,
label: ...$L... t,
list-max: list-max(x.f[x];L),
CollapseTHENA: Error :CollapseTHENA,
RepeatFor: Error :RepeatFor,
es-prior-interface: prior(X),
bag: bag(T),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
Unfold: Error :Unfold,
D: Error :D,
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
collect_filter: collect_filter(),
es-interface-accum: es-interface-accum(f;x;X),
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
es-collect-filter-max-aux: es-collect-filter-max-aux(X;size;v.num[v];v.P[v];v.f[v]),
Subst': Error :Subst',
combination: Combination(n;T),
listp: A List,
RepUR: Error :RepUR,
compose: f o g,
IdLnk: IdLnk,
es-filter-image: f[X]
Lemmas :
list_subtype_base,
set_subtype_base,
int_subtype_base,
product_subtype_base,
list-max-map,
map_wf,
map-map,
es-interface-predecessors-sqequal,
length-map,
sq_stable__assert,
pos_length2,
list-max_wf,
mapfilter_wf,
collect-filter-max-val,
uiff_inversion,
es-base-E_wf,
es-interface-subtype_rel,
es-interface-predecessors-equal-subtype,
decidable__assert,
sq_stable_from_decidable,
eq_int_wf,
assert_elim,
map-class-val,
es-E-interface_wf,
Id_wf,
es-interface-predecessors_wf,
filter_wf,
squash_wf,
es-loc_wf,
length_wf1,
bool_subtype_base,
subtype_base_sq,
length_wf_nat,
intensional-universe_wf,
assert-eq-id,
filter_type,
l_member_wf,
list-subtype,
subtype_rel_set,
subtype_rel_list,
nat_plus_properties,
filter_wf_top,
es-interface-val_wf2,
es-interface-val_wf,
l_all_wf,
list-set-type2,
sq_stable__equal,
sq_stable_wf,
property-from-l_member,
length-map-sq,
le_wf,
es-locl_wf,
band_wf,
not_wf,
alle-lt_wf,
es-first-at_wf,
is-collect-filter-max,
subtype_rel_product,
subtype_rel_simple_product,
bfalse_wf,
unit_wf,
btrue_wf,
subtype_rel_self,
es-interface-subtype_rel2,
is-map-class,
rev_implies_wf,
iff_wf,
nat_wf,
pi1_wf,
pi2_wf,
es-collect-filter-max_wf,
map-class_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
eclass_wf,
nat_plus_wf,
bool_wf,
es-interface-extensionality,
pi1_wf_top,
top_wf,
member_wf,
subtype_rel_wf,
assert_wf,
false_wf,
ifthenelse_wf,
in-eclass_wf,
true_wf,
es-interface-top,
eclass-val_wf
\mforall{}[Info,A,B:Type]. \mforall{}[g:B {}\mrightarrow{} A]. \mforall{}[h:A {}\mrightarrow{} B].
(\mforall{}[f:A {}\mrightarrow{} \mBbbZ{}]. \mforall{}[X:EClass(B)]. \mforall{}[size:\mBbbN{}\msupplus{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}].
((<fst(tr)
, fst(snd(tr))
, h[snd(snd(tr))]> where tr from Collect(size v's from (g[x] where x from X)
with maximum num[v] such that P[v]
return <num[v],n,v> with n = maximum f[v]))
= Collect(size x's from X with maximum num[g[x]] such that P[g[x]]
return <num[g[x]],n,x> with n = maximum f[g[x]]))) supposing
((\mforall{}b:B. (h[g[b]] = b)) and
(\mforall{}a:A. (g[h[a]] = a)))
Date html generated:
2011_08_16-PM-05_33_13
Last ObjectModification:
2010_12_22-PM-09_36_31
Home
Index