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Proof step 22 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 = ROOT_INO, ∀ ino. (ino ∈ dirs \ orphans(dirs, files) ↔ ino ∈ (dirs \ (orphans(dirs, files) -- m)) -- m) ∧ (ino ∈ dirs \ orphans(dirs, files) → (dirs \ orphans(dirs, files))[ino] = ((dirs \ (orphans(dirs, files) -- m)) -- m)[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs ⊦ m = ROOT_INO, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) → dirs[ino] = ((dirs \ (orphans(dirs, files) -- m)) -- m)[ino])

Rule argument

Additional information

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