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Theorem abs-path-h
∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ((abs(tree, ino) * D))(dirs) ⊦ ispath(p, ino, dirs, files) ↔ p ∈ tree
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
abs-delorphans
,
abs-meta-h
,
abs-nlinks-h
,
abs-paths-eq
,
abs-unshared-h
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 15
Used lemmas:
abs-fnode
,
entries-dom1
,
entries-recdel
,
abs-dnode
,
abs-is-file
,
Used spec theorems:
Used simplifier rules:
afs-base
/
expath-eps
directory-tree
/
nil-in
directory-tree
/
split-in
list
/path/
a
afs-base
/
valid-dir-ino
afs-base
/
expath-rec
list
/path/
c
abstract-dir
/
elim
abstract-dir
/
sel-09
abstract-dir
/
sel-03
directory-tree-fids
/
fids-dnode
maplet
/dir-heap/
map-in
maplet
/dir-heap/
at-eq
maplet
/dir-heap/
ex3-shift
directory-tree
/
one-at
directory-tree
/
one-ind
directory-tree-fids
/
fids-str
bag-union
/fidbag/
in-one
directory-tree-fids
/
fids-fnode
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/
sep-com
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
emp-sep
heap-sep
/dir-heap/
prop-shift
directory-tree
/
one-inf
file-id-data
/
elim
file-id-data
/
inj