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Proof step 16 from proof crash-neutral-evict (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs ⊦ m = ROOT_INO, dirs \ orphans(dirs, files) = (dirs -- m) \ (orphans(dirs, files) -- m) ∧ files \ orphans(dirs, files) = files \ (orphans(dirs, files) -- m)

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ dirs[ino] = mkdir(n, md, 0, m, ∅) ∧ afs-cons(dirs, files) → orphans(dirs -- ino, files) = orphans(dirs, files) -- ino; (s)