{ 
[Info:Type]. [es:EO+(Info)]. [A:Type]. [X:EClass(A)]. [Q:E(X) 
].
[P:A ]. [e:E(X)].
uiff((v
mapfilter(
e.X(e);e'.Q[e'];
(X)(e)).
P[v]);e'e.(e' 
X)
(Q[e'])
(P[X(e')])) }
{ Proof }
Definitions occuring in Statement :
es-interface-predecessors: (X)(e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
alle-le: ee'.P[e],
assert: b,
bool: ,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
so_apply: x[s],
implies: P Q,
lambda: x.A[x],
function: x:A B[x],
universe: Type,
mapfilter: mapfilter(f;P;L),
l_all: (xL.P[x])
Definitions :
es-locl: (e <loc e'),
listp: A List
,
combination: Combination(n;T),
map: map(f;as),
real: 
,
grp_car: |g|,
int: 
,
length: ||as||,
select: l[i],
sq_type: SQType(T),
cand: A c
B,
nat: 
,
nil: [],
filter: filter(P;l),
list: type List,
exists: 
x:A. B[x],
intensional-universe: IType,
or: P 
Q,
guard: {T},
eq_knd: a = b,
fpf-dom: x dom(f),
in-eclass: e X,
fpf: a:A fp-> B[a],
eclass-val: X(e),
so_apply: x[s],
es-loc: loc(e),
Id: Id,
es-interface-predecessors: (X)(e),
mapfilter: mapfilter(f;P;L),
strong-subtype: strong-subtype(A;B),
set: {x:A| B[x]} ,
le: A B,
ge: i 
j ,
not: 
A,
less_than: a < b,
rev_implies: P 
Q,
iff: P Q,
l_member: (x l),
es-le: e loc e' ,
prop: 
,
so_lambda: 
x.t[x],
pair: <a, b>,
l_all: (xL.P[x]),
void: Void,
false: False,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: b,
implies: P Q,
alle-le: ee'.P[e],
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
union: left + right,
es-E-interface: E(X),
bool: ,
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
member: t T,
equal: s = t,
event-ordering+: EO+(Info),
tactic: Error :tactic,
cond-class: [X?Y],
sq_stable: SqStable(P),
Knd: Knd,
IdLnk: IdLnk,
cons: [car / cdr],
btrue: tt,
isl: isl(x),
can-apply: can-apply(f;x),
limited-type: LimitedType,
append: as @ bs,
hd: hd(l),
last: last(L),
remove-repeats: remove-repeats(eq;L),
squash: 
T,
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
sqequal: s ~ t
Lemmas :
sq_stable__assert,
es-le-loc,
event_ordering_wf,
squash_wf,
nat_wf,
l_member-settype,
l_member_subtype,
member-interface-predecessors-subtype,
member-mapfilter,
implies_functionality_wrt_iff,
all_functionality_wrt_iff,
iff_functionality_wrt_iff,
bool_subtype_base,
assert_elim,
assert_wf,
es-E_wf,
es-le_wf,
alle-le_wf,
l_all_wf,
assert_witness,
uiff_wf,
l_member_wf,
es-interface-top,
member_wf,
eclass_wf,
es-E-interface_wf,
bool_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
l_all_wf2,
es-interface-predecessors_wf,
Id_wf,
mapfilter_wf,
es-loc_wf,
eclass-val_wf,
subtype_rel_wf,
false_wf,
ifthenelse_wf,
in-eclass_wf,
true_wf,
rev_implies_wf,
iff_wf,
intensional-universe_wf,
list-subtype,
es-interface-val_wf2,
subtype_base_sq,
filter_wf,
map_wf,
length_wf1
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Q:E(X) {}\mrightarrow{} \mBbbB{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[e:E(X)].
uiff((\mforall{}v\mmember{}mapfilter(\mlambda{}e.X(e);\mlambda{}e'.Q[e'];\mleq{}(X)(e)).\muparrow{}P[v]);\mforall{}e'\mleq{}e.(\muparrow{}e' \mmember{}\msubb{} X) {}\mRightarrow{} (\muparrow{}Q[e']) {}\mRightarrow{} (\muparrow{}P[X(e')]))
Date html generated:
2011_08_16-PM-05_23_03
Last ObjectModification:
2011_06_20-AM-01_22_16
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