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Proof step 4 from proof abs-orphans-diff-datakeys (previous step)

⊦ ino0 ∈ orphans(abs-dirs(fs, ri), abs-files(fs, ri \ datakeys(inodekey(ino), n, ri))) ↔ ino0 ∈ orphans(abs-dirs(fs, ri), abs-files(fs, ri))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 6:
⊦ ino0 ∈ orphans(abs-dirs(fs, ri), abs-files(fs, ri \ datakeys(inodekey(ino), n, ri))) ↔ valid-ino(ino0, abs-dirs(fs, ri), abs-files(fs, ri)) ∧ links(ino0, abs-dirs(fs, ri)) = ∅ ∧ ino0 ≠ ROOT_INO

Rule argument

spec: afs-base name: orphans seq: ⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO subst: [files, dirs, ino] → [abs-files(fs, ri), abs-dirs(fs, ri), ino0] flags: <all paths>

Additional information

Used terms: abs-files(fs, ri), abs-dirs(fs, ri), ino0