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Theorem abs-paths-eq
abs(tree, ino0)(dirs), ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ispath(p0, ino0, ino1, dirs, files), ispath(p1, ino0, ino1, dirs, files), ino1 ∈ dirs ⊦ p0 = p1
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: 28
Proof steps: 71
Used lemmas:
absc-emp
,
entries-recdel
,
entries-dom2
,
entries-dom1
,
abs-is-dnode
,
absc-path
,
path-unfold
,
abs-dir-h
,
abs-path-h
,
Used spec theorems:
list
/path/
longest-common-prefix
afs-base
/
path-split
directory-tree
/
split-at
Used simplifier rules:
afs-base
/
isexpath
list
/path/
app-01
list-data
/path/
elim-list-c
abstract-dir
/
elim
maplet
/dir-heap/
ex1
directory-tree
/
notdir-notin
list
/path/
e
abstract-dir
/
sel-04
abstract-dir
/
sel-09
abstract-dir
/
sel-03
maplet
/dir-heap/
at-eq
directory-tree
/
dnode-elim
heap-sep
/dir-heap/
true-and
store
/dir-entries/
Del-at
directory-tree-base
/
Del-at
heap-sep
/dir-heap/
true-rev
store
/dir-entries/
Del-in
directory-tree-base
/
Del-in
maplet
/dir-heap/
ex1-shift
maplet
/dir-heap/
map-in
list
/path/
app-02
afs-base
/
path-inj
afs-base
/
valid-dir-ino
afs-base
/
path-rec
directory-tree
/
split-in
list
/path/
e-01
list
/path/
c
directory-tree
/
one-ind
directory-tree
/
isdnode
maplet
/dir-heap/
ex3-shift
maplet
/dir-heap/
map-same
heap-sep
/dir-heap/
false-sep
heap-sep
/dir-heap/
false-and
heap-sep
/dir-heap/
falseH
directory-tree
/
nil-at
heap-sep
/dir-heap/
prop-shift
heap-sep
/dir-heap/
emp-sep
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and
heap-sep
/dir-heap/
prop
list
/path/
app
list
/path/
a
directory-tree
/
one-at
directory-tree
/
nil-in
afs-base
/
path-in-dirs
directory-tree
/
at-dnode