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Theorem D-ext

⊦ dirs = abs-dirs(fs, ri) ↔ (∀ ino. (ino ∈ dirs ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory) ∧ (ino ∈ dirs → dirs[ino] = abs-dir(ino, fs, ri)))

Type: A user defined theorem
Validity: The proof is valid.
Features: lss, ss,
Comment:
Used by: abs-dirs-del-data, abs-dirs-del-dentry, abs-dirs-del-dir, abs-dirs-del-file, abs-dirs-del-orphans, abs-dirs-deldatakeys-1, abs-dirs-deldatakeys-2, abs-dirs-drop, abs-dirs-gc-copy, abs-dirs-orphans, abs-dirs-trunc, abs-dirs-unused-adrs,
Used by units in proved state: aubifs-refine,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: dir, at-dirs, in-dirs,
Used spec theorems:
- heap/dir-heap/ext
Used simplifier rules: