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Theorem abs-tree
∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files, ∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files, ((abs(tree0, ino) * D0))(dirs), ((abs(tree1, ino) * D1))(dirs) ⊦ tree0 = tree1
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: 12
Proof steps: 56
Used lemmas:
entries-dom1
,
entries-dom2
,
entries-recdel
,
abs-fnode
,
abs-dnode
,
Used spec theorems:
directory-tree
/
tree-ext
Used simplifier rules:
directory-tree
/
nil-at
directory-tree
/
nil-in
abstract-dir
/
elim
directory-tree
/
meta
file-id-data
/
elim
file-id-data
/
inj
maplet
/dir-heap/
map-in
directory-tree
/
fid
directory-tree
/
isfnode
directory-tree
/
isdnode
directory-tree
/
split-in
list
/path/
c
abstract-dir
/
sel-04
abstract-dir
/
sel-09
abstract-dir
/
sel-03
maplet
/dir-heap/
eq-objs
list
/path/
a
directory-tree
/
at-dnode
heap-sep
/dir-heap/
true-and
heap-sep
/dir-heap/
true-rev
directory-tree-fids
/
fids-str
bag-union
/fidbag/
in-one
directory-tree-fids
/
fids-fnode
heap-sep
/dir-heap/
emp-sep
directory-tree
/
one-inf
directory-tree-fids
/
fids-dnode
directory-tree
/
one-at
heap-sep
/dir-heap/
prop
heap-sep
/dir-heap/
and
heap-sep
/dir-heap/
sep-com
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
prop-shift
maplet
/dir-heap/
ex3-shift
directory-tree
/
one-ind