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PROSA - Formally Proven Schedulability Analysis
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RT-PROOFS
PROSA - Formally Proven Schedulability Analysis
Commits
eda66272
Commit
eda66272
authored
3 years ago
by
Pierre Roux
Committed by
Björn Brandenburg
2 years ago
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Remove subn_abba
Too specific.
parent
e3567e95
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1 merge request
!212
various cleanups and simplifications in util
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2 changed files
analysis/facts/transform/swaps.v
+3
-4
3 additions, 4 deletions
analysis/facts/transform/swaps.v
util/nat.v
+0
-7
0 additions, 7 deletions
util/nat.v
with
3 additions
and
11 deletions
analysis/facts/transform/swaps.v
+
3
−
4
View file @
eda66272
...
...
@@ -248,10 +248,9 @@ Section SwappedFacts.
rewrite
/
service
!
service_in_replaced
//
/
service_at
//
/
replace_at
//.
rewrite
ifT
//
ifT
//
ifF
;
last
by
apply
ltn_eqF
;
exact
.
rewrite
subn_abba
//.
rewrite
-
(
service_split_at_point
_
_
_
t1
_)
/
service_at
//.
apply
leq_trans
with
(
n
:=
service_during
sched
j
0
t1
+
service_in
j
(
sched
t1
));
[
rewrite
addnC
|];
by
apply
leq_addr
.
have
service_in_t1
:
service_in
j
(
sched
t1
)
<=
service_during
sched
j
0
t
.
{
by
rewrite
-
(
service_split_at_point
_
_
_
t1
_)
//
addnAC
leq_addl
.
}
by
rewrite
subnK
?(
leq_trans
service_in_t1
)
?leq_addr
//
addnK
.
Qed
.
(** Finally, we note that, trivially, jobs that are not involved in
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util/nat.v
+
0
−
7
View file @
eda66272
...
...
@@ -26,13 +26,6 @@ Section NatLemmas.
m
<=
p
-
n
.
Proof
.
by
intros
;
lia
.
Qed
.
(** Simplify [n + a - b + b - a = n] if [n >= b]. *)
Lemma
subn_abba
:
forall
n
a
b
,
n
>=
b
->
n
+
a
-
b
+
b
-
a
=
n
.
Proof
.
by
intros
;
lia
.
Qed
.
(** We can drop additive terms on the lesser side of an inequality. *)
Lemma
leq_addk
:
forall
m
n
k
,
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