{ 
[es:EO]. [P:E 
]. [Q:{e:E| 
(P e)} ].
(eo-restrict(eo-restrict(es;P);Q) = eo-restrict(es;
e.((P e) 
(Q e)))) }
{ Proof }
Definitions occuring in Statement :
eo-restrict: eo-restrict(eo;P),
es-E: E,
event_ordering: EO,
band: p q,
assert: b,
bool: ,
uall: [x:A]. B[x],
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
equal: s = t
Definitions :
ifthenelse: if b then t else f fi ,
rec_select_update: rec_select_update{rec_select_update_compseq_tag_def:o}(y; v; x; r),
universe: Type,
prop: 
,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record-select: r.x,
infix_ap: x f y,
dep-isect: Error :dep-isect,
record+: record+,
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
all: x:A. B[x],
bool: ,
set: {x:A| B[x]} ,
assert: b,
es-E: E,
eo-restrict: eo-restrict(eo;P),
lambda: x.A[x],
band: p q,
apply: f a,
function: x:A B[x],
event_ordering: EO,
equal: s = t,
member: t 
T,
axiom: Ax,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
fpf-dom: x dom(f),
squash: 
T,
void: Void,
so_lambda: 
x.t[x],
atom: Atom,
list: type List,
nat: 
,
exists: 
x:A. B[x],
Id: Id,
token: "$token",
top: Top,
record: record(x.T[x]),
sq_type: SQType(T),
limited-type: LimitedType,
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
set_blt: a < b,
grp_blt: a < b,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
bimplies: p 
q,
bor: p 
q,
bnot: b,
int: 
,
unit: Unit,
so_apply: x[s],
union: left + right,
or: P Q,
guard: {T},
l_member: (x l),
true: True,
false: False,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
es-base-E: es-base-E(es),
eo-reset-dom: eo-reset-dom(es;d),
iff: P 
Q,
rev_implies: P Q,
implies: P Q,
es-dom: es-dom(es)
Lemmas :
es-dom_wf,
ifthenelse_wf,
false_wf,
band_wf,
es-base-E_wf,
bfalse_wf,
not_wf,
bnot_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
eqtt_to_assert,
true_wf,
eo-reset-dom-reset-dom,
rev_implies_wf,
iff_wf,
assert_of_band,
member_wf,
subtype_rel_wf,
assert_functionality_wrt_uiff,
bnot_thru_band,
assert_of_bor,
or_functionality_wrt_uiff,
bor_wf,
eo-reset-dom_wf,
top_wf,
l_member_wf,
Id_wf,
record_wf,
record+_wf,
Error :dep-isect_wf,
btrue_wf,
btrue_neq_bfalse,
assert_elim,
squash_wf,
eo-restrict_wf,
assert_wf,
es-E_wf,
bool_wf,
event_ordering_wf
\mforall{}[es:EO]. \mforall{}[P:E {}\mrightarrow{} \mBbbB{}]. \mforall{}[Q:\{e:E| \muparrow{}(P e)\} {}\mrightarrow{} \mBbbB{}].
(eo-restrict(eo-restrict(es;P);Q) = eo-restrict(es;\mlambda{}e.((P e) \mwedge{}\msubb{} (Q e))))
Date html generated:
2011_08_16-AM-10_22_33
Last ObjectModification:
2011_01_20-AM-00_47_03
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