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Proof step 5 from proof orphans-del-dir (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# links(ino, dirs) = 0, dirs[ino] = mkdir(n, md, 0, m, ∅), afs-cons(dirs, files), ino ∈ dirs ⊦ ino0 ∈ orphans(dirs -- ino, files) ↔ ino0 ≠ ino ∧ ino0 ∈ orphans(dirs, files), ino = ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ ns -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ ns; (s)