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Theorem inv-rmdir
afs-cons(dirs, files), pre-rmdir(p_inode, c_inode, dent, dirs, files) ⊦ ⟪afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)
Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
cache-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 141
Used lemmas:
internal-inode-sync
,
lastlink-rename
,
lastlink-move
,
afs-cons-reduce
,
afs-cons-inode-sync
,
drop-nlink
,
rmdir
,
Used spec theorems:
set-union
/dir-entries/
del-size
set-basic
/dir-entries/
Extension
afs-base
/
afs-cons
Used simplifier rules:
dentry
/
elim
inode
/
elim
abstract-dir
/
elim
afs-base
/
getinode
abstract-dir
/
upd-08
abstract-dir
/
upd-03
abstract-dir
/
upd-09
nat
/
elim-pred-c
nat
/
lep
nat-basic
/
oz
abstract-dir
/
upd-05
afs-base
/
afs-cons-root-dir
abstract-file
/
elim
afs-base
/
afs-cons-pagesize
afs-base
/
links-modmeta
afs-base
/
links-del-entry
afs-base
/
links-modmeta-write2
afs-base
/
afs-cons-links-empty
nat-basic
/
one
nat
/
one-02
nat
/
succ-01
set-union
/alink-set/
del-e-02
set-union
/alink-set/
del-in
afs-asm
/
Del-size
afs-base
/
links
alink
/
sel-02
alink
/
sel-01
store
/dir-entries/
size
nat
/
pred-03
afs-base
/
subdirs-write
afs-base
/
subdirs-modmeta
afs-base
/
subdirs-putother
nat-basic
/
z-01
afs-base
/
subdirs-del-mod-size
nat
/
add-01
nat-basic
/
add-base
nat-basic
/
a
nat-basic
/
c
set-union
/dir-entries/
del-in
nat-basic
/
eq-02
store
/dir-entries/
Del-in
store
/dir-entries/
Del-at
store
/dir-entries/
Del-empty
heap
/file-heap/
at-write
heap
/file-heap/
overwrite
heap
/dir-heap/
overwrite-split
abstract-dir
/
upd-04
inode
/
sel-02
afs-base
/
afs-cons-in-next
afs-base
/
afs-cons-notfile
heap
/dir-heap/
in-write
set-basic
/alink-set/
size-zero
set-basic
/alink-set/
size-zero-01
set-basic
/alink-set/
size-zero-02
afs-base
/
links-nonempty
abstract-dir
/
updsel-24
abstract-dir
/
updsel-20
heap
/dir-heap/
overwrite
nat
/
not-zero
afs-base
/
valid-pagesize
set-basic
/dir-entries/
Size-empty
set-basic
/dir-entries/
size-zero-02
store
/dir-entries/
Size-empty
set-basic
/dir-entries/
In-empty
afs-base
/
subdirs
nat-basic
/
one-01
nat
/
le-def
nat
/
ge
abstract-dir
/
updsel-13
heap
/dir-heap/
at-write
abstract-dir
/
inj
store
/dir-entries/
empty
store
/dir-entries/
In-empty
afs-base
/
afs-cons-dir-nlink
error-class
/
ecommit
abstract-dir
/
sel-08
abstract-dir
/
sel-03
abstract-dir
/
sel-05
abstract-dir
/
sel-09
inode
/
sel-03
inode
/
sel-10
inode
/
sel-11
inode
/
sel-04
afs-base
/
valid-dir-ino
afs-pre
/
valid-dir-inode
afs-base
/
dir-empty
dentry
/
test-02
dentry
/
sel-04
afs-base
/
valid-ino
afs-base
/
valid-parent-ino
afs-base
/
valid-dentry-with-parent
inode
/
sel-01
dentry
/
sel-05
afs-pre
/
pre-rmdir