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Proof step 23 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, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) → dirs[ino] = ((dirs \ (orphans(dirs, files) -- m)) -- m)[ino])

User applied rule cut formula

And obtained the following new goals

Proof step 24:
# 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])
Proof step 27:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), ino = m, afs-cons(dirs, files), m ∈ dirs ⊦ m = ROOT_INO, m ∈ orphans(dirs, files), (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (ino ∈ dirs ∧ ¬ ino ∈ orphans(dirs, files) → dirs[ino] = ((dirs \ (orphans(dirs, files) -- m)) -- m)[ino])

Rule argument

fma: ¬ m ∈ orphans(dirs, files) → ino ≠ m

Additional information

Used formulas: ¬ m ∈ orphans(dirs, files) → ino ≠ m