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Theorem abs-nlinks-h
∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, abs(tree, ino0)(dirs), ino1 ∈ files, ino0 ∈ dirs ⊦ ⌜ino1⌝ ∈ tree.fids ↔ links(ino1, dirs) ≠ ∅
Type: A user defined theorem
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: 22
Proof steps: 52
Used lemmas:
abs-is-file
,
abs-dir-h
,
abs-has-rootpath
,
entries-recdel
,
entries-dom1
,
entries-dom2
,
abs-dnode
,
absc-path
,
path-unfold
,
abs-fnode
,
abs-path-h
,
Used spec theorems:
directory-tree-fids
/
fids-in
list
/path/
lastdiv-rew
afs-base
/
expath
afs-base
/
path-split
directory-tree
/
dnode-onein
set-basic
/alink-set/
Extension
directory-tree
/
dnode-elim-strong
directory-tree-fids
/
fids-path
directory-tree
/
split-at
Used simplifier rules:
directory-tree
/
nil-at
directory-tree
/
nil-in
afs-base
/
expath-eps
heap-sep
/dir-heap/
emp
directory-tree-fids
/
fids-fnode
bag-union
/fidbag/
in-one
file-id-data
/
inj
heap
/dir-heap/
in-emp
afs-base
/
path-in-dirs
list
/path/
e-02
afs-base
/
path-one
abstract-dir
/
elim
heap-sep
/dir-heap/
true-and
heap-sep
/dir-heap/
true-rev
alink
/
sel-01
alink
/
sel-02
abstract-dir
/
inj
file-id-data
/
sel
heap-sep
/dir-heap/
emp-sep
heap-sep
/dir-heap/
false-rev
heap-sep
/dir-heap/
falseH
set-basic
/alink-set/
In-empty
afs-base
/
links
alink
/
elim
set-basic
/alink-set/
size-zero-01
set-basic
/alink-set/
size-zero
afs-base
/
links-nonempty
afs-base
/
isexpath
abstract-dir
/
sel-04
abstract-dir
/
sel-09
abstract-dir
/
sel-03
maplet
/dir-heap/
map-in
maplet
/dir-heap/
at-eq
heap-sep
/dir-heap/
prop
heap-sep
/dir-heap/
and
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
prop-shift
maplet
/dir-heap/
ex3-shift
maplet
/dir-heap/
ex1
directory-tree
/
one-ind
list
/path/
a
directory-tree
/
split-in
list
/path/
Last
directory-tree
/
one-at
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com