Nuprl Lemma : equal-next-world
0,22
postcript
pdf
D
:Dsys,
i
:Id,
s1
,
s2
:M(
i
).state,
k1
,
k2
:Knd,
v1
:d-decl(
D
;
i
)(
k1
),
v2
:d-decl(
D
;
i
)(
k2
),
m1
:{
m
:M(
i
).Msg| source(mlnk(
m
)) =
i
} List.
Feasible(
D
)
<
s1
,doact(
k1
;
v1
),
m1
> = next-world-state(
D
;
i
;
s2
;
k2
;
v2
)
d-world-state(
D
;
i
)
{
s1
= (
x
.M(
i
).ef(
k2
,
x
,
s2
,
v2
)?
s2
(
x
))
{
&
k1
=
k2
{
&
v1
=
v2
d-decl(
D
;
i
)(
k2
)
{
&
m1
= filter(
m
.source(mlnk(
m
)) =
i
;M(
i
).sends(
k2
,
s2
,
v2
))}
latex
Definitions
t
T
,
{
T
}
,
mlnk(
m
)
,
Msg(
da
)
,
Msg(
M
)
,
P
&
Q
,
Prop
,
next-world-state(
D
;
i
;
s
;
k
;
v
)
,
x
:
A
.
B
(
x
)
,
P
Q
,
doact(
k
;
v
)
,
M
.Msg
,
Action(
dec
)
,
d-world-state(
D
;
i
)
,
2of(
t
)
,
1of(
t
)
,
x
.
t
(
x
)
Lemmas
unit
wf
,
inr
equal
,
action
wf
,
pi1
wf
,
pi2
wf
,
doact
wf
,
next-world-state
wf
,
d-world-state
wf
,
d-feasible
wf
,
lsrc
wf
,
Id
wf
,
d-m
wf
,
ma-msg
wf
,
d-decl
wf
,
Knd
wf
,
ma-st
wf
,
dsys
wf
origin