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Proof step 8 from proof orphans-del-dir (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# 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

Rule argument

Additional information

Used simplifier rules: valid-ino: ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files;%links-deldir: ⊦ ino0 ∈ dirs ∧ dirs[ino0] = mkdir(m, md, n, n0, ∅) → links(ino, dirs -- ino0) = links(ino, dirs);% ⊦ ino ∈ dirs -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ dirs; (s)