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Theorem links-del-entry
⊦ ino0 ∈ dirs → links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries -- str)]) = (str ∈ entries ∧ entries[str] = ino ⊃ links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str) ;links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) )
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
links-delother-subdirs
,
links-delsame-mod-subdirs
,
Used by units in proved state:
cache-asm
,
afs-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 20
Used lemmas:
links
,
Used spec theorems:
set-basic
/alink-set/
Extension
Used simplifier rules:
store
/dir-entries/
notin-del-notin
set-union
/alink-set/
Delete
alink
/
elim
abstract-dir
/
elim
alink
/
inj
heap
/dir-heap/
at-write
heap
/dir-heap/
in-write
abstract-dir
/
inj
store
/dir-entries/
Del-in
store
/dir-entries/
Del-at
store
/dir-entries/
Del-other-data
store
/dir-entries/
Del-at-strong