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Theorem abs-acyclic
⊦ abs(tree, ROOT_INO)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, m, m0, entries) ∧ str ∈ entries ∧ ispath(p, ROOT_INO, ino, dirs, files) → entries[str] ≠ ROOT_INO
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
refine-rmdir
,
refine-unlink
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 34
Used lemmas:
fid-file
,
path-in-eq
,
path-in
,
make-abs-fold-work
,
Used spec theorems:
vfs-abs
/
path-unfold
vfs-abs
/
absc-path
vfs-abs
/
entries-recdel
vfs-abs
/
abs-is-dnode
vfs-abs
/
abs-dir-h
afs-base
/
path-trans
directory-tree
/
split-at
vfs-abs
/
absc-dnode
Used simplifier rules:
afs-base
/
afs-cons-dir-nlink
maplet
/dir-heap/
ex1
directory-tree
/
dnode-elim
vfs-abs
/
entries-dom2
vfs-abs
/
entries-dom1
afs-base
/
afs-cons-notfile
afs-base
/
path-one
maplet
/dir-heap/
at-eq
abstract-dir
/
inj
abstract-dir
/
elim
afs-base
/
afs-cons-root-dir
vfs-abs
/
abs-is-file
list
/path/
Last
directory-tree
/
one-at
vfs-abs
/
abs-fnode
heap-sep
/dir-heap/
and
heap-sep
/dir-heap/
emp
heap-sep
/dir-heap/
prop
directory-tree-base
/
disj
afs-base
/
path-in-dirs
heap
/dir-heap/
in-emp
directory-tree
/
isdnode
afs-base
/
isexpath
maplet
/dir-heap/
ex3-shift
heap-sep
/dir-heap/
prop-shift
maplet
/dir-heap/
map-same
heap-sep
/dir-heap/
false-sep
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
heap-sep
/dir-heap/
false-and
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
falseH
directory-tree
/
nil-at
directory-tree-base
/
dnode-inj
afs-base
/
path-here
afs-base
/
valid-ino
maplet
/dir-heap/
map-in
vfs-abs
/
absc-emp
heap-sep
/dir-heap/
true-rev
heap-sep
/dir-heap/
true-and
heap-sep
/dir-heap/
emp-sep