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Proof step 9 from proof orphans-del-dir (previous step)

# links(ino, dirs) = 0, dirs[ino] = mkdir(n, md, 0, m, ∅), afs-cons(dirs, files), ino ∈ dirs ⊦ (ino0 ≠ ino ∧ ino0 ∈ dirs ∨ ino0 ∈ files) ∧ links(ino0, dirs) = ∅ ∧ ino0 ≠ ROOT_INO ↔ ino0 ≠ ino ∧ ino0 ∈ orphans(dirs, files), ino = ROOT_INO

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 11:
# links(ino, dirs) = 0, dirs[ino] = mkdir(n, md, 0, m, ∅), afs-cons(dirs, files), ino ∈ dirs ⊦ (ino0 ≠ ino ∧ ino0 ∈ dirs ∨ ino0 ∈ files) ∧ links(ino0, dirs) = ∅ ∧ ino0 ≠ ROOT_INO ↔ ino0 ≠ ino ∧ valid-ino(ino0, dirs, files) ∧ links(ino0, dirs) = ∅ ∧ ino0 ≠ ROOT_INO, ino = ROOT_INO

Rule argument

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

Additional information

Used terms: files, dirs, ino0