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Theorem abs-meta-h
∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files, ((abs(tree, ino) * D))(dirs), ispath(p, ino, dirs, files), fs = abs-files(files) ⊦ meta(p, tree, fs) = meta(p, ino, dirs, files)
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: 6
Proof steps: 19
Used lemmas:
abs-dnode
,
abs-files-at
,
abs-is-file
,
absc-path
,
path-unfold
,
abs-path-h
,
abs-dir-h
,
Used spec theorems:
afs-base
/
expath
posix-base
/
meta-dir
Used simplifier rules:
afs-base
/
meta-path
afs-base
/
isexpath
maplet
/dir-heap/
ex1-shift
directory-tree
/
isfnode
directory-tree
/
fid
posix-base
/
meta-file
file-data
/
elim
directory-tree-fids
/
fids-path
file-data
/
inj
afs-base
/
meta-file
afs-base
/
meta-dir
directory-tree
/
dnode-elim
maplet
/dir-heap/
map-in
directory-tree
/
isdnode
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
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
maplet
/dir-heap/
at-eq
abstract-dir
/
inj
abstract-dir
/
elim