{ 
[A,B,C:Type]. [f:Id 
A B bag(C)]. [abag:bag(A)]. [bbag:bag(B)].
[l:Id].
(concat-lifting2-loc(f;abag;bbag;l) 
bag(C)) }
{ Proof }
Definitions occuring in Statement :
concat-lifting2-loc: concat-lifting2-loc(f;abag;bbag;loc),
Id: Id,
uall: [x:A]. B[x],
member: t T,
function: x:A B[x],
universe: Type,
bag: bag(T)
Definitions :
natural_number: $n,
lambda: 
x.A[x],
select: l[i],
cons: [car / cdr],
nil: [],
Try: Error :Try,
Complete: Error :Complete,
Unfold: Error :Unfold,
RepeatFor: Error :RepeatFor,
CollapseTHEN: Error :CollapseTHEN,
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
member: t T,
isect: 
x:A. B[x],
bag: bag(T),
uall: [x:A]. B[x],
function: x:A B[x],
Id: Id,
universe: Type,
equal: s = t,
concat-lifting2-loc: concat-lifting2-loc(f;abag;bbag;loc),
axiom: Ax,
all: x:A. B[x],
concat-lifting-loc: concat-lifting-loc(n;bags;loc;f),
funtype: funtype(n;A;T),
quotient: x,y:A//B[x; y],
subtype_rel: A 
r B,
uiff: uiff(P;Q),
and: P 
Q,
product: x:A 
B[x],
uimplies: b supposing a,
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A 
B,
strong-subtype: strong-subtype(A;B),
atom: Atom$n,
fpf: a:A fp-> B[a],
eclass: EClass(A[eo; e]),
int: 
,
nat: 
,
subtype: S T,
rationals: 
,
real: 
,
set: {x:A| B[x]} ,
false: False,
implies: P 
Q,
void: Void,
prop: 
,
p-outcome: Outcome,
int_seg: {i..j
},
list: type List,
lelt: i j < k,
length: ||as||,
hd: hd(l),
tl: tl(l),
decidable: Dec(P),
path-goes-thru: x-f*-y thru i,
cut-order: a (X;f) b,
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
es-E-interface: E(X),
same-thread: same-thread(es;p;e;e'),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
apply: f a,
exists: 
x:A. B[x],
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],
alle-lt: e<e'.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-E: E,
es-causl: (e < e'),
infix_ap: x f y,
consensus-rcv: consensus-rcv(V;A),
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,
consensus-state3: consensus-state3(T),
l_disjoint: l_disjoint(T;l1;l2),
MaName: MaName,
Knd: Knd,
IdLnk: IdLnk,
fset-closed: (s closed under fs),
fset: FSet{T},
f-subset: xs ys,
fset-member: a s,
dstype: dstype(TypeNames; d; a),
i-closed: i-closed(I),
i-finite: i-finite(I),
sq_exists: x:{A| B[x]},
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
limited-type: LimitedType,
fun-connected: y is f*(x),
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
squash: 
T,
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
cmp-le: cmp-le(cmp;x;y),
l_contains: A B,
nat_plus: 
,
or: P 
Q,
union: left + right,
sq_type: SQType(T),
guard: {T},
permutation: permutation(T;L1;L2),
suptype: suptype(S; T),
primrec: primrec(n;b;c),
ycomb: Y,
sqequal: s ~ t,
top: Top,
eq_int: (i =
j)
Lemmas :
ycomb-unroll,
funtype_wf,
subtype_rel_wf,
permutation_wf,
Id_wf,
concat-lifting-loc_wf,
not_wf,
false_wf,
nat_wf,
member_wf,
le_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
length_wf1,
int_seg_wf,
bag_wf,
select_wf
\mforall{}[A,B,C:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[abag:bag(A)]. \mforall{}[bbag:bag(B)]. \mforall{}[l:Id].
(concat-lifting2-loc(f;abag;bbag;l) \mmember{} bag(C))
Date html generated:
2011_08_17-PM-06_13_18
Last ObjectModification:
2011_06_01-PM-07_56_32
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