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Theorem inv-write
of-cons(of, dirs, files), dom of < ino, afs-cons(dirs, files), n ≤ # buf ⊦ ⟪vfs_write#(fd, buf, user; n, err, of, dirs, files, asynced)⟫ (of-cons(of, dirs, files) ∧ dom of < ino ∧ afs-cons(dirs, files))
Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 32
Proof steps: 597
Used lemmas:
write-page
,
write-block
,
of-cons-reduce
,
write-loop
,
write
,
write-term
,
Used spec theorems:
nat-div
/
rax
afs-asm
/
afs-cons-reduce
store
/open-files/
At-other
Used simplifier rules:
nat
/
le-ls-simp
afs-pre
/
pre-iget
abstract-file
/
elim
afs-pre
/
pre-truncate
nat
/
le
nat
/
zero-02
nat
/
eq-02
nat-div
/
cond
nat-basic
/
eq-02
afs-base
/
valid-pagesize
afs-base
/
valid-ino
afs-base
/
dir-empty
abstract-dir
/
elim
array-copy
/buffer/
size-fill-h
nat
/
let
afs-pre
/
pre-readpage
array
/buffer/
Size-mkarray
store
/file-content/
At-other
afs-pre
/
pre-writepage
store
/file-content/
in-neq
store
/file-content/
At-in-out
store
/file-content/
In-insert
store
/file-content/
At-same
array-copy
/buffer/
size-copy
page
/
emptypage-size
nat
/
cancel-01
nat-div
/
mod-le-02
nat
/
lep-02
inode
/
elim
inode
/
inj
afs-base
/
afs-cons-root-dir
inode
/
sel-03
inode
/
sel-10
inode
/
sel-04
afs-base
/
valid-file-ino
afs-pre
/
valid-file-inode
afs-base
/
valid-dir-ino
afs-pre
/
valid-dir-inode
afs-pre
/
valid-wb-inode
afs-pre
/
pre-write-inode
nat
/
elim-sub
nat-basic
/
l
nat
/
lep
nat-basic
/
lf-02
nat
/
ls-le-simp
nat
/
le-def
store
/open-files/
At-other
store
/open-files/
insin
abstract-file
/
upd-05
abstract-file
/
sel-01
afs-base
/
getinode
buffer-option
/
test-03
nat
/
ler
page
/
page-size
min-max
/
min-same
inode
/
upd-11
abstract-file
/
upd-06
heap
/file-heap/
overwrite
abstract-file
/
upd-04
inode
/
sel-11
afs-base
/
in-upto
nat-mult
/
mult-a
nat-mult
/
mult-c
afs-base
/
at-upto
nat-basic
/
f
error-class
/
esuccess
abstract-file
/
inj
nat-basic
/
lf-01
afs-base
/
afs-cons-pagesize
afs-base
/
afs-cons-file-nlink
afs-base
/
afs-cons-notfile
afs-base
/
afs-cons-in-next
store
/open-files/
in-neq
store
/open-files/
At-same
file
/
inj
nat
/
ge
error-class
/
not-esuccess
file
/
sel
store
/open-files/
k-At-same
store
/open-files/
In-insert
nat
/
lels
store
/open-files/
ins
file
/
upd-03
store+set
/open-files/
dom-add-in
store+set
/open-files/
dom-ins
nat-basic
/
c
nat-basic
/
a
nat-basic
/
add-base
file
/
elim
heap
/dir-heap/
in-write
inode
/
sel-02
vfs-base
/
of-cons-file
heap
/file-heap/
in-write
abstract-file
/
sel-06
abstract-file
/
sel-02
abstract-file
/
sel-07
heap
/file-heap/
at-write
vfs-base
/
of-cons-notdir
inode
/
sel-01
nat
/
lez
store
/open-files/
notmemlookup