{ 
[Info:Type]. [es:EO+(Info)]. [X:EClass(
)]. [e:E].
(
e(X)
= if e 
X then if e prior(X) then prior(X)(e)(X) else 0 fi + X(e)
if e prior(X) then prior(X)(e)(X)
else 0
fi ) }
{ Proof }
Definitions occuring in Statement :
es-interface-sum: e(X),
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
ifthenelse: if b then t else f fi ,
uall: [x:A]. B[x],
add: n + m,
natural_number: $n,
int: ,
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
es-interface-sum: e(X),
member: t T,
so_lambda: 
x y.t[x; y],
ifthenelse: if b then t else f fi ,
top: Top,
all: x:A. B[x],
implies: P 
Q,
btrue: tt,
prop: 
,
es-E-interface: E(X),
bfalse: ff,
rev_implies: P 
Q,
iff: P Q,
and: P 
Q,
so_apply: x[s1;s2],
bool: 
,
unit: Unit,
uimplies: b supposing a,
subtype: S 
T,
it: 
,
guard: {T}
Lemmas :
es-E_wf,
eclass_wf,
event-ordering+_wf,
event-ordering+_inc,
in-eclass_wf,
bool_wf,
iff_weakening_uiff,
assert_wf,
eqtt_to_assert,
es-prior-interface_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
top_wf,
es-interface-local-state_wf,
eclass-val_wf2,
eclass-val_wf,
not_wf,
uiff_transitivity,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
es-interface-local-state-cases
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(\mBbbZ{})]. \mforall{}[e:E].
(\mSigma{}\mleq{}e(X)
= if e \mmember{}\msubb{} X then if e \mmember{}\msubb{} prior(X) then \mSigma{}\mleq{}prior(X)(e)(X) else 0 fi + X(e)
if e \mmember{}\msubb{} prior(X) then \mSigma{}\mleq{}prior(X)(e)(X)
else 0
fi )
Date html generated:
2011_08_16-PM-05_35_00
Last ObjectModification:
2011_06_20-AM-01_27_53
Home
Index