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Theorem abs-has-rootpath-h
⊦ ((abs(tree, ino0) * {dirs0} ))(dirs) ∧ ino1 ∈ dirs ∧ ¬ ino1 ∈ dirs0 → (∃ p. ispath(p, ino0, ino1, dirs, files))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
abs-has-rootpath
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 24
Proof steps: 51
Used lemmas:
entries-dom2
,
entries-dom1
,
abs-empty
,
entries-any
,
abs-dnode
,
abs-fnode
,
Used spec theorems:
directory-tree
/
tree-induction
heap-sep
/dir-heap/
sep
maplet
/dir-heap/
maplet
heap-sep
/dir-heap/
sep-split-interactive
maplet
/dir-heap/
map-del
store
/dir-entries/
Subset
Used simplifier rules:
maplet
/dir-heap/
ex3-shift
abstract-dir
/
elim
store
/dir-entries/
subset-empty
directory-tree-base
/
In-empty
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
afs-base
/
valid-ino
afs-base
/
path-here
heap-sep
/dir-heap/
this
heap
/dir-heap/
disj-singleton-write
heap
/dir-heap/
in-write
heap
/dir-heap/
in-alloc
store
/directory-tree-inst/
neq
directory-tree-base
/
At-same
store
/directory-tree-inst/
insin
heap
/dir-heap/
in-emp
heap-sep
/dir-heap/
emp-sep
heap-sep
/dir-heap/
this-emp
list
/path/
a
heap
/dir-heap/
at-uni
maplet
/dir-heap/
map-in
heap
/dir-heap/
in-uni
afs-base
/
valid-dir-ino
afs-base
/
path-rec
list
/path/
c
heap
/dir-heap/
disj-l
abstract-dir
/
inj
maplet
/dir-heap/
at-eq
store
/dir-entries/
insin
store
/dir-entries/
At-same
afs-base
/
path-uni
heap
/dir-heap/
disj-r
directory-tree-base
/
Size-insert
nat-basic
/
s-04
oelem
/nat-set/
irreflexivity
nat-basic
/
a
nat-basic
/
c
store
/dir-entries/
At-in-out
store
/dir-entries/
In-insert
directory-tree-base
/
In-insert
store
/directory-tree-inst/
At-in-out
afs-base
/
path-uni-com
heap-sep
/dir-heap/
precise-split-l
store
/dir-entries/
sub-ref
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com