{ 
[B:Type]. [n:
]. [m:n + 1]. [A:n 
Type]. [bags:k:n bag(A k)].
[f:funtype(n - m;
x.(A (x + m));bag(B))]. [b:B].
(bag-member(B;b;concat-lifting-list(n;bags) m f)
lst:k:{m..n
} (A k)
(([k:{m..n}]. bag-member(A k;lst k;bags k))
bag-member(B;b;uncurry-gen(n) m (x.f) lst))) }
{ Proof }
Definitions occuring in Statement :
concat-lifting-list: concat-lifting-list(n;bags),
uncurry-gen: uncurry-gen(n),
int_seg: {i..j},
nat: ,
uall: [x:A]. B[x],
exists: x:A. B[x],
iff: P Q,
squash: T,
and: P Q,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type,
bag-member: bag-member(T;x;bs),
bag: bag(T),
funtype: funtype(n;A;T)
Definitions :
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try,
Complete: Error :Complete,
CollapseTHEN: Error :CollapseTHEN,
bag: bag(T),
lambda: x.A[x],
Auto: Error :Auto,
set: {x:A| B[x]} ,
squash: T,
function: x:A B[x],
implies: P Q,
product: x:A 
B[x],
and: P Q,
iff: P Q,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
int_seg: {i..j},
universe: Type,
nat: ,
apply: f a,
quotient: x,y:A//B[x; y],
funtype: funtype(n;A;T),
primrec: primrec(n;b;c),
member: t 
T,
equal: s = t,
all: x:A. B[x],
subtract: n - m,
int: 
,
subtype: S 
T,
rationals: 
,
real: 
,
le: A 
B,
not: 
A,
false: False,
void: Void,
less_than: a < b,
add: n + m,
minus: -n,
lelt: i j < k,
prop: 
,
subtype_rel: A r B,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i 
j ,
natural_number: $n,
strong-subtype: strong-subtype(A;B),
grp_car: |g|,
exists: x:A. B[x],
bag-member: bag-member(T;x;bs),
so_lambda: 
x.t[x],
rev_implies: P Q,
true: True,
concat-lifting-list: concat-lifting-list(n;bags),
ycomb: Y,
fpf: a:A fp-> B[a],
eclass: EClass(A[eo; e]),
uncurry-gen: uncurry-gen(n),
limited-type: LimitedType,
sq_type: SQType(T),
guard: {T},
RepUR: Error :RepUR,
Unfold: Error :Unfold,
sqequal: s ~ t,
eq_int: (i =
j),
btrue: tt,
MaAuto: Error :MaAuto,
lifting-gen-list-rev: Error :lifting-gen-list-rev,
bag-union: bag-union(bbs),
top: Top,
bool: 
,
single-bag: {x},
concat: concat(ll),
append: as @ bs,
list: type List,
nil: [],
permutation: permutation(T;L1;L2),
es-E-interface: E(X),
map: map(f;as),
ifthenelse: if b then t else f fi ,
sq_stable: SqStable(P),
classrel: v X(e),
fpf-sub: f g,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
rnonneg: rnonneg(r),
req: x = y,
bfalse: ff,
pair: <a, b>,
bag-combine: 
xbs.f[x],
qabs: |r|,
filter: filter(P;l),
bnot: 
b,
assert: 
b,
bor: p 
q,
band: p q,
bimplies: p q,
es-ble: e loc e',
es-bless: e <loc e',
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
name_eq: name_eq(x;y),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_atom: eq_atom$n(x;y),
eq_type: eq_type(T;T'),
b-exists: (i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
infix_ap: x f y,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
eq_atom: x =a y,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
RepeatFor: Error :RepeatFor,
tactic: Error :tactic,
l_member: (x l),
or: P Q,
union: left + right,
so_apply: x[s],
unit: Unit,
le_int: i z j,
lt_int: i <z j,
Knd: Knd,
locl: locl(a),
Id: Id,
IdLnk: IdLnk,
cand: A c B,
intensional-universe: IType,
gt: i > j,
apply_gen: apply_gen(n;lst),
BHyp: Error :BHyp,
suptype: suptype(S; T)
Lemmas :
apply_gen_wf,
apply_larger_list,
apply_uncurry,
gt_wf,
btrue_neq_bfalse,
bool_cases,
intensional-universe_wf,
int_sq,
ifthenelse_wf,
eqtt_to_assert,
eqff_to_assert,
uiff_transitivity,
assert_of_bnot,
not_functionality_wrt_uiff,
bnot_wf,
UnknownObject
true_wf,
primrec_wf,
temp-lifting-gen-list-rev_wf,
bag-combine_wf,
UnknownObject
assert_of_eq_int,
iff_weakening_uiff,
iff_functionality_wrt_iff,
assert_wf,
iff_imp_equal_bool,
bfalse_wf,
sq_stable__bag-member,
eq_int_eq_true,
bool_wf,
bool_subtype_base,
eq_int_wf,
ycomb-unroll,
bag-subtype-list,
subtype_rel_wf,
top_wf,
permutation_wf,
append_nil_sq,
int_seg_properties,
subtype_base_sq,
int_subtype_base,
nat_ind_tp,
nat_properties,
ge_wf,
concat-lifting-list_wf,
uncurry-gen_wf2,
rev_implies_wf,
iff_wf,
squash_wf,
uall_wf,
bag-member_wf,
funtype_wf,
bag_wf,
int_seg_wf,
nat_wf,
member_wf,
le_wf,
not_wf,
false_wf
\mforall{}[B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[m:\mBbbN{}n + 1]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[bags:k:\mBbbN{}n {}\mrightarrow{} bag(A k)].
\mforall{}[f:funtype(n - m;\mlambda{}x.(A (x + m));bag(B))]. \mforall{}[b:B].
(bag-member(B;b;concat-lifting-list(n;bags) m f)
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}lst:k:\{m..n\msupminus{}\} {}\mrightarrow{} (A k)
((\mforall{}[k:\{m..n\msupminus{}\}]. bag-member(A k;lst k;bags k))
\mwedge{} bag-member(B;b;uncurry-gen(n) m (\mlambda{}x.f) lst)))
Date html generated:
2011_08_17-PM-06_08_19
Last ObjectModification:
2011_06_01-PM-06_38_34
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