{ 
[B:Type]. [n:
]. [A:n 
Type]. [bags:k:n bag(A k)].
[f:funtype(n;A;bag(B))]. [b:B].
(bag-member(B;b;concat-lifting(n;f;bags))
lst:k:n (A k)
(([k:n]. bag-member(A k;lst k;bags k))
bag-member(B;b;uncurry-rev(n;f) lst))) }
{ Proof }
Definitions occuring in Statement :
concat-lifting: concat-lifting(n;f;bags),
uncurry-rev: uncurry-rev(n;f),
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,
function: x:A B[x],
natural_number: $n,
universe: Type,
bag-member: bag-member(T;x;bs),
bag: bag(T),
funtype: funtype(n;A;T)
Definitions :
D: Error :D,
Unfold: Error :Unfold,
CollapseTHENA: Error :CollapseTHENA,
sqequal: s ~ t,
subtract: n - m,
equal: s = t,
function: x:A B[x],
int_seg: {i..j},
universe: Type,
lambda: 
x.A[x],
apply: f a,
add: n + m,
natural_number: $n,
Try: Error :Try,
Complete: Error :Complete,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
quotient: x,y:A//B[x; y],
bag: bag(T),
set: {x:A| B[x]} ,
squash: T,
implies: P Q,
product: x:A 
B[x],
and: P Q,
iff: P Q,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
nat: ,
funtype: funtype(n;A;T),
primrec: primrec(n;b;c),
member: t 
T,
all: x:A. B[x],
int: 
,
subtype: S 
T,
grp_car: |g|,
real: 
,
concat-lifting: concat-lifting(n;f;bags),
rationals: 
,
lelt: i 
j < k,
less_than: a < b,
le: A B,
not: 
A,
false: False,
prop: 
,
void: Void,
subtype_rel: A r B,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i 
j ,
strong-subtype: strong-subtype(A;B),
ycomb: Y,
p-outcome: Outcome,
fpf: a:A fp-> B[a],
eclass: EClass(A[eo; e]),
sq_type: SQType(T),
guard: {T},
pair: <a, b>,
exists: x:A. B[x],
bag-member: bag-member(T;x;bs),
so_lambda: 
x.t[x],
rev_implies: P Q,
concat-lifting-list: concat-lifting-list(n;bags),
uncurry-rev: uncurry-rev(n;f),
uncurry-gen: uncurry-gen(n),
true: True
Lemmas :
uncurry-rev_wf,
concat-lifting-list_wf,
rev_implies_wf,
iff_wf,
squash_wf,
uall_wf,
bag-member_wf,
concat-lifting-list-member,
nat_wf,
member_wf,
bag_wf,
funtype_wf,
subtype_rel_wf,
subtype_base_sq,
int_subtype_base,
int_seg_wf,
le_wf,
not_wf,
false_wf
\mforall{}[B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[bags:k:\mBbbN{}n {}\mrightarrow{} bag(A k)]. \mforall{}[f:funtype(n;A;bag(B))]. \mforall{}[b:B].
(bag-member(B;b;concat-lifting(n;f;bags))
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}lst:k:\mBbbN{}n {}\mrightarrow{} (A k)
((\mforall{}[k:\mBbbN{}n]. bag-member(A k;lst k;bags k)) \mwedge{} bag-member(B;b;uncurry-rev(n;f) lst)))
Date html generated:
2011_08_17-PM-06_08_54
Last ObjectModification:
2011_06_01-PM-07_38_49
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