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Theorem afs-cons-mkdir-ino
afs-cons(dirs, files), pre-mkdir(p_inode, dent, md, dirs, files), ¬ ino ∈ dirs, ¬ ino ∈ files, ino ≠ 0 ⊦ ⟪afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs)⟫ afs-cons(dirs, files)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
inv-mkdir
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 47
Used lemmas:
afs-cons-reduce
,
mkdir-ino
,
Used spec theorems:
afs-base
/
links-putnew
heap
/dir-heap/
at-alloc
set-basic
/dir-entries/
Extension
set-union
/dir-entries/
size-eq-ext
Used simplifier rules:
afs-base
/
valid-dir-ino
afs-pre
/
valid-dir-inode
afs-base
/
valid-parent-ino
afs-base
/
valid-negdentry
afs-pre
/
pre-mkdir
dentry
/
elim-02
dentry
/
test-01
inode
/
elim
abstract-dir
/
elim
afs-base
/
afs-cons-root-dir
abstract-dir
/
upd-08
abstract-dir
/
sel-08
abstract-dir
/
upd-03
abstract-dir
/
sel-03
abstract-dir
/
upd-09
afs-base
/
valid-pagesize
afs-base
/
valid-ino
afs-base
/
dir-empty
abstract-dir
/
updsel-24
abstract-dir
/
updsel-20
heap
/dir-heap/
overwrite
abstract-dir
/
updsel-13
dentry
/
sel-03
abstract-file
/
elim
afs-base
/
afs-cons-pagesize
afs-base
/
afs-cons-nlink0-notin
afs-base
/
links-modmeta
afs-base
/
links-add-entry
afs-base
/
links-inc-nsubdirs
set-basic
/dir-entries/
size-zero-01
set-basic
/dir-entries/
size-zero
set-basic
/alink-set/
size-one-01
set-basic
/dir-entries/
In-empty
afs-base
/
subdirs-putother
nat-basic
/
eq-01
store
/dir-entries/
Size-insert
store
/dir-entries/
neq
store
/dir-entries/
In-insert
store
/dir-entries/
k-At-same
afs-base
/
afs-cons-links-empty
afs-base
/
afs-cons-notfile
set-basic
/alink-set/
size-zero-01
abstract-dir
/
sel-05
set-basic
/dir-entries/
size-ins
nat-basic
/
a
nat-basic
/
c
store
/dir-entries/
notmemlookup
set-basic
/dir-entries/
In-insert
store
/dir-entries/
in-neq
store
/dir-entries/
At-in-out
store
/dir-entries/
insin
store
/dir-entries/
At-same
abstract-dir
/
sel-09
heap
/dir-heap/
in-alloc
afs-base
/
subdirs
heap
/dir-heap/
in-write
heap
/dir-heap/
at-alloc
heap
/dir-heap/
at-write
afs-base
/
afs-cons-dir-nlink
abstract-dir
/
inj
store
/dir-entries/
Size-empty
store
/dir-entries/
In-empty
afs-base
/
afs-cons-non0
afs-base
/
afs-cons-in-next