Nuprl Lemma : acks-between-reqs
11,40
postcript
pdf
es
:ES,
ff
:FIFO,
is_req
,
is_ack
:(E
),
awaiting
,
owes_ack
:(Id
Id
Id).
(
ff
.C
r Id)
(
i
,
j
:
ff
.C. @
i
(
awaiting
(
i
,
j
):
) & @
i
(
owes_ack
(
i
,
j
):
))
(
i
:
ff
.C,
e
:E. (
ff
.R(
i
,
e
))
(loc(
e
) =
i
Id))
(
e
:E. Dec(
is_req
(
e
)) & Dec(
is_ack
(
e
)))
(
i
,
j
:
ff
.C,
e
:E. Dec(
ff
.S(
i
,
j
,
e
)))
(
i
,
j
:
ff
.C,
e
:E. (
ff
.S(
i
,
j
,
e
))
(loc(
e
) =
i
Id))
plus-ify{i:l}(
es
;
ff
;
is_req
;
is_ack
;
awaiting
;
owes_ack
)
(
sndr
,
rcvr
:
ff
.C,
e
,
e'
:E.
[
e
:
sndr
is_req
rcvr
]
[
e'
:
sndr
is_req
rcvr
]
(
e
<
e'
)
x
(
e
,
e'
].[
x
:
sndr
is_ack
rcvr
])
latex
Definitions
P
Q
,
e
loc
e'
,
e
(
e1
,
e2
].
P
(
e
)
,
P
Q
,
P
Q
,
{
T
}
,
SQType(
T
)
,
A
c
B
,
x
:
A
.
B
(
x
)
,
A
,
(
e
<loc
e'
)
,
t
T
,
P
&
Q
,
P
Q
,
,
x
:
A
.
B
(
x
)
,
if
b
then
t
else
f
fi
,
b
,
tt
,
@
i
(
x
:
T
)
,
Dec(
P
)
,
False
,
plus-ify{i:l}(
es
;
ff
;
is_req
;
is_ack
;
awaiting
;
owes_ack
)
Lemmas
awaiting-2-ff
,
rcv-it
wf
,
es-le
wf
,
es-locl
wf
,
equal-bnot
,
Id
sq
,
es-after
wf
,
es-when
wf
,
es-locl-iff
,
es-loc-pred
,
inconsistent-bool-eq
,
decidable
equal
bool
,
change-lemma2
,
snd-it-loc
,
event
system
wf
,
FIFO
wf
,
bool
wf
,
es-dtype
wf
,
fifoR
wf
,
decidable
wf
,
es-loc
wf
,
Id
wf
,
fifoS
wf
,
plus-ify
wf
,
fifoC
wf
,
es-E
wf
,
snd-it
wf
,
es-causl
wf
origin