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Theorem prepost-scan-all
ubi-io-inv(apebs), unique-sqns(apebs) ⊦ ⟪ubi_scan_all#(LEB_SIZE, apebs; recs, wlar, q, bflipset, n1; n2, n3, nx, err)⟫ scan-all-inv(# apebs, apebs, recs, wlar, q, bflipset, nx, n1, err)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
inv-recover
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 66
Proof steps: 494
Used lemmas:
lf-valid-eraseq-stronger-notin-recs
,
ls-max
,
lf-valid-recs-max
,
lf-valid-recs-valid-peb
,
lf-valid-recs-in-apebs
,
lf-valid-recs-sqns-vidhdr
,
lf-valid-recs-notin-eraseq
,
ubi-io-inv-fwd
,
nat-sum-leq
,
scan-all
,
Used spec theorems:
ubi-crash-recovery-base
/
valid-eraseq-stronger-next-append-lref
valid-peb
/
valid-peb0
ubi-crash-recovery-base
/
valid-eraseq-stronger-next-append-none
ubi-crash-recovery-base
/
valid-eraseq-stronger-prev-append-lref
ubi-base
/
unique-sqns-2-valid-pebs
ubi-base
/
valid-wl-next-valid-update
ubi-crash-recovery-base
/
indices-set-erasing
ubi-base
/
valid-wl-next-valid-erase
ubi-base
/
valid-wl-next-valid-use
valid-peb
/
valid-peb2
ubi-base
/
valid-wl-next-invalid-erase
Used simplifier rules:
list
/erasequeue-base/
Last
list
/nat-list-set/
c
wlarray
/
elim-update-status
array-copy
/wlarray-base/
size-fill
array
/wlarray-base/
Size-mkarray
list-dup
/nat-list-set/
e-01
nat-list-less
/
ls-base
ubi-crash-recovery-base
/
indices-erasing-base
array-copy
/apebs/
subarray-zero
ubi-base
/
valid-global-sqn-array-0
array-copy
/wlarray-base/
subarray-zero
ubi-base
/
valid-eraseq-array-0
ubi-base
/
bitflips-cons-empty
ubi-crash-recovery-base
/
valid-eraseq-stronger-base
ubi-base
/
valid-wl-array-0
ubi-crash-recovery-base
/
valid-recs-sqns-emptyset
ubi-crash-recovery-base
/
valid-recs-emptyset
nat
/
ls-01
nat
/
le-ls-simp
ubi-crash-recovery-base
/
scan-all-inv
nat
/
elim-sub
ubi-io-pre
/
isbad-pre
wlstatus
/
disj-02
wlstatus
/
disj-06
apeb
/
elim
wlentry
/
elim-02
ubi-base
/
valid-wl-next-bad
valid-peb
/
valid-peb0-bad
ubi-io-pre
/
read-echdr-pre
wlentry
/
sel-04
ubi-crash-recovery-base
/
indices-erasing-rec
nat-list-less
/
ls-prepend-bound-add1
list
/nat-list-set/
a
nat-list-less
/
ls-bound-notin
list-dup
/nat-list-set/
dups-cons
valid-peb
/
valid-peb0-invalid-ehdr
aecheader
/
elim
ubi-io-pre
/
read-vidhdr-pre
wlstatus
/
disj-05
wlstatus
/
disj-01
ubi-base
/
valid-wl-next-free
valid-peb
/
valid-peb0-vidhdr-empty
avidheader
/
elim
ubi-base
/
bflipset-subarray-erase-old-add
set-union
/nat-set/
del-addeq-05
nat
/
ls-le-simp
ubi-base
/
valid-global-sqn-next-max
nat
/
anti
recovery-entry
/
elim
ubi-base
/
bflipset-subarray-erase-old
ubi-base
/
valid-eraseq-prev-erasing
ubi-crash-recovery-base
/
valid-recs-next-update
array
/wlarray-base/
cngetput
array-copy
/wlarray-base/
subarray-elim
array-copy
/apebs/
subarray-elim
nat-basic
/
succ-03
nat-basic
/
neq-03
nat
/
fle-01
nat
/
lep
nat-basic
/
succ
avidheader
/
inj
aecheader
/
test-02
valid-peb
/
not-valid-peb2-explicit-0
apeb
/
sel-04
aecheader
/
sel
ubi-crash-recovery-base
/
valid-recs-sqns-update
datasize
/
datasize-le-fwd
avidheader
/
sel-07
avidheader
/
sel-09
array-copy
/buffer/
copy-exact
ubi-io-inv
/
peb-inv-size
apeb
/
sel-06
nat
/
zero
nat
/
ge
array-splice
/buffer/
range-eq-0
error
/
disj-91
error-class
/
ecommit
array
/buffer/
Size-mkarray
nat
/
ler
nat-basic
/
add-base
ubi-io-pre
/
read-data-pre
apeb
/
inj
nat
/
fle
nat-basic
/
f
ubi-crash-recovery-base
/
valid-recs-next-samerecs
ubi-base
/
valid-eraseq-next-erasing
lebadress
/
sel-01
lebadress
/
sel-02
ubi-crash-recovery-base
/
indices-set-erasing
ubi-crash-recovery-base
/
valid-recs-in-nonempty-sqns
ubi-crash-recovery-base
/
valid-eraseq-stronger-next-append-lref
valid-peb
/
valid-peb-unique
sqns
/
valid-sqns-rec
bag-max
/
bag-union-one
bag-union
/nat-bag/
union-ass
bag-union
/nat-bag/
union-com
nat
/
gr-def
nat-basic
/
lf-02
nat-basic
/
lf
oelem
/nat-set/
transitivity
avidheader
/
sel-10
nat-basic
/
ls-02
valid-peb
/
valid-peb0-imp-valid-peb
avidheader
/
sel-06
avidheader
/
sel-08
ubi-base
/
bflipset-subarray-add
nat-basic
/
l-02
nat
/
le-def
ubi-crash-recovery-base
/
valid-recs-next-add
avidheader
/
test-03
avidheader
/
disj-02
sqns
/
valid-sqns-subarray
nat
/
lels-03
array-copy
/wlarray-base/
size-subarray
array-copy
/apebs/
size-subarray
ubi-crash-recovery-base
/
valid-eraseq-stronger-next
ubi-base
/
bflipset-subarray-next
ubi-base
/
valid-eraseqw-subarray-shift
wlstatus
/
disj-03
ubi-crash-recovery-base
/
indices-erasing-write-notin
nat-list-less
/
ls-add
array
/wlarray-base/
cputput
wlentry
/
updsel-02
array
/wlarray-base/
Put-same
error-class
/
esuccess
nat
/
lez
array
/wlarray-base/
Size-put
nat
/
le-add
ubi-crash-recovery-base
/
valid-eraseq-stronger-next-append-none
list
/erasequeue-base/
a
ubi-base
/
valid-global-sqn-next
apeb
/
sel-05
apeb
/
sel-08
valid-peb
/
valid-peb0-invalid-vhdr
nat
/
lels
nat-basic
/
lf-01
error-class
/
not-esuccess
nat
/
succ-01
nat-basic
/
a
nat-basic
/
c
nat-basic
/
s-04
nat-basic
/
l-01
nat-basic
/
l
oelem
/nat-set/
irreflexivity