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Theorem crash-neutral-rmdir

pre-rmdir(p_inode, c_inode, dent, dirs, files), afs-cons(dirs, files), asynced, dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files) ⊦ ⟨afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Type: A proof obligation
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: 5
Proof steps: 112
Used lemmas: internal-inode-sync, drop-nlink, rmdir,
Used spec theorems:
- Used simplifier rules:
  - dentry/elim
  - inode/elim
  - abstract-dir/elim
  - afs-base/afs-cons-dir-nlink
  - afs-base/getinode
  - abstract-dir/upd-08
  - abstract-dir/upd-03
  - abstract-dir/upd-09
  - nat/elim-pred-c
  - nat/lep
  - nat-basic/c
  - nat-basic/a
  - nat-basic/oz
  - abstract-dir/upd-05
  - heap/file-heap/overwrite
  - heap/file-heap/at-write
  - inode/sel-02
  - inode/inj
  - error-class/efail
  - abstract-dir/upd-04
  - heap/dir-heap/overwrite-split
  - heap/dir-heap/in-write
  - afs-base/afs-cons-notfile
  - set-basic/alink-set/size-zero
  - set-basic/alink-set/size-zero-01
  - afs-base/links-nonempty
  - set-basic/alink-set/size-zero-02
  - abstract-dir/updsel-24
  - abstract-dir/updsel-20
  - heap/dir-heap/overwrite
  - nat/not-zero
  - nat-basic/one-01
  - nat/le-def
  - nat/ge
  - abstract-dir/updsel-13
  - heap/dir-heap/at-write
  - abstract-dir/inj
  - abstract-dir/sel-08
  - abstract-dir/sel-03
  - abstract-dir/sel-05
  - abstract-dir/sel-09
  - inode/sel-03
  - inode/sel-10
  - inode/sel-11
  - inode/sel-04
  - afs-base/valid-dir-ino
  - afs-pre/valid-dir-inode
  - afs-base/dir-empty
  - dentry/test-02
  - dentry/sel-04
  - afs-base/valid-ino
  - afs-base/valid-parent-ino
  - afs-base/valid-dentry-with-parent
  - inode/sel-01
  - dentry/sel-05
  - afs-pre/pre-rmdir