{ 
[Info,B:Type]. [n:
]. [A:n 
Type]. [Xs:k:n EClass(A k)].
[f:Id k:n (A k) B]. [F:Id k:n bag(A k) bag(B)].
[es:EO+(Info)]. [e:E]. [v:B].
uiff(v 
F|Loc; Xs|(e);
vs:k:n (A k)
((k:n. vs[k] Xs[k](e))
(v = (f loc(e) vs))))
supposing x:Id. v:B. bs:k:n bag(A k).
(bag-member(B;v;F x bs)
vs:k:n (A k)
((k:n. bag-member(A k;vs k;bs k)) (v = (f x vs)))) }
{ Proof }
Definitions occuring in Statement :
simple-loc-comb: F|Loc; Xs|,
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
int_seg: {i..j
},
nat: ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
all: 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: $n,
universe: Type,
equal: s = t,
bag-member: bag-member(T;x;bs),
bag: bag(T)
Definitions :
Try: Error :Try,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
uall: [x:A]. B[x],
set: {x:A| B[x]} ,
nat: ,
squash: T,
isect: 
x:A. B[x],
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
universe: Type,
function: x:A B[x],
int_seg: {i..j},
eclass: EClass(A[eo; e]),
so_lambda: 
x y.t[x; y],
bag: bag(T),
quotient: x,y:A//B[x; y],
apply: f a,
Id: Id,
all: x:A. B[x],
iff: P Q,
exists: x:A. B[x],
equal: s = t,
bag-member: bag-member(T;x;bs),
prop: 
,
implies: P Q,
event-ordering+: EO+(Info),
record+: record+,
dep-isect: Error :dep-isect,
es-E: E,
event_ordering: EO,
classrel: v X(e),
simple-loc-comb: F|Loc; Xs|,
so_apply: x[s],
true: True,
member: t T,
int: 
,
le: A 
B,
not: 
A,
false: False,
subtype_rel: A 
r B,
less_than: a < b,
ge: i 
j ,
strong-subtype: strong-subtype(A;B),
assert: 
b,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
rev_implies: P Q,
eq_atom: eq_atom$n(x;y),
eq_atom: x =a y,
record-select: r.x,
natural_number: $n,
subtype: S T,
grp_car: |g|,
real: 
,
limited-type: LimitedType,
es-loc: loc(e),
lambda: x.A[x],
sq_stable: SqStable(P),
CollapseTHENA: Error :CollapseTHENA,
RepUR: Error :RepUR,
lelt: i j < k,
fpf: a:A fp-> B[a],
top: Top
Lemmas :
Error :es-interface-top,
subtype_rel_wf,
member_wf,
es-loc_wf,
iff_wf,
bag-member_wf,
bag_wf,
Id_wf,
eclass_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
nat_wf,
classrel_wf,
int_seg_wf,
squash_wf,
sq_stable__classrel,
simple-loc-comb_wf
\mforall{}[Info,B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[Xs:k:\mBbbN{}n {}\mrightarrow{} EClass(A k)]. \mforall{}[f:Id {}\mrightarrow{} k:\mBbbN{}n {}\mrightarrow{} (A k) {}\mrightarrow{} B].
\mforall{}[F:Id {}\mrightarrow{} k:\mBbbN{}n {}\mrightarrow{} bag(A k) {}\mrightarrow{} bag(B)].
\mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:B].
uiff(v \mmember{} F|Loc; Xs|(e);\mdownarrow{}\mexists{}vs:k:\mBbbN{}n {}\mrightarrow{} (A k). ((\mforall{}k:\mBbbN{}n. vs[k] \mmember{} Xs[k](e)) \mwedge{} (v = (f loc(e) vs))))
supposing \mforall{}x:Id. \mforall{}v:B. \mforall{}bs:k:\mBbbN{}n {}\mrightarrow{} bag(A k).
(bag-member(B;v;F x bs)
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}vs:k:\mBbbN{}n {}\mrightarrow{} (A k). ((\mforall{}k:\mBbbN{}n. bag-member(A k;vs k;bs k)) \mwedge{} (v = (f x vs))))
Date html generated:
2011_08_16-AM-11_38_30
Last ObjectModification:
2011_05_23-PM-06_30_08
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