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Theorem path-fid
⊦ ispath(p, ino0, ino1, dirs, files) ∧ ino1 ∈ files ∧ ¬ ino1 ∈ dirs ∧ p ∈ tree ∧ ((abs(tree, ino0) * D))(dirs) → tree[p] = fnode(⌜ino1⌝ )
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 10
Used lemmas:
entries-unfold
,
entries-dom1
,
entries-dom2
,
abs-dnode
,
abs-is-file
,
Used spec theorems:
Used simplifier rules:
directory-tree
/
nil-at
directory-tree
/
nil-in
afs-base
/
path-here
afs-base
/
valid-ino
afs-base
/
valid-dir-ino
afs-base
/
path-rec
directory-tree
/
split-in
list
/path/
c
abstract-dir
/
elim
directory-tree
/
one-inf
abstract-dir
/
sel-09
abstract-dir
/
sel-03
directory-tree
/
one-at
afs-base
/
path-in-dirs
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
list
/path/
a
directory-tree-inst
/
read-notin
directory-tree
/
at-dnode
directory-tree
/
one-ind
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
store
/dir-entries/
At-same
store
/dir-entries/
In-insert
directory-tree-base
/
In-insert
store
/dir-entries/
Size-insert
directory-tree-base
/
At-same