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Theorem abs-dirs-del-dentry

⊦ inodekey(ino) ∈ ri ∧ ino ≠ 0 ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri -- dentrykey(ino, str)) = abs-dirs(fs, ri) [ino, mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri) -- str) ]

Type: A user defined theorem
Validity: The proof is valid.
Features: s,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 7
Used lemmas: at-children, in-children, C-ext, D-inj, dir, at-dirs, in-dirs, D-ext,
Used spec theorems:
- Used simplifier rules:
  - heap/dir-heap/at-write
  - key/disj-02
  - heap/dir-heap/in-write
  - store/dir-entries/Del-in
  - store/dir-entries/Del-at
  - store/node-index/Del-at-strong
  - key/inj-01
  - store/node-index/Del-at
  - store/node-index/Del-in