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Proof step 24 from proof crash-neutral-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs, ¬ m ∈ orphans(dirs, files) → ino ≠ m ⊦ m = ROOT_INO, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) → dirs[ino] = ((dirs \ (orphans(dirs, files) -- m)) -- m)[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs, ino ∈ dirs ⊦ dirs[ino] = (dirs \ (orphans(dirs, files) -- m))[ino], ino = m, m = ROOT_INO, ino ∈ orphans(dirs, files)

Rule argument

Additional information

Used simplifier rules: ino ∈ dirs ⊦ ino ≠ ino0 → (dirs -- ino0)[ino] = dirs[ino]; (s)% ⊦ ino ∈ ns -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ ns; (s)% ⊦ ino ∈ dirs \ ns ↔ ino ∈ dirs ∧ ¬ ino ∈ ns; (s)