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Proof step 7 from proof abs-orphans (previous step)

afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ⊦ ino ∈ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0, ino = ROOT_INO

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 9:
afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) ⊦ valid-ino(ino, abs-dirs(fs, ri), abs-files(fs, ri)) ∧ links(ino, abs-dirs(fs, ri)) = ∅ ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0, ino = 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), ino] flags: <all paths>

Additional information

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