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Proof step 17 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, dirs \ orphans(dirs, files) = (dirs -- m) \ (orphans(dirs, files) -- m) ∧ files \ orphans(dirs, files) = files \ (orphans(dirs, files) -- m)

User applied rule case distinction

And obtained the following new goals

Proof step 18:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs ⊦ dirs \ orphans(dirs, files) = (dirs -- m) \ (orphans(dirs, files) -- m), m = ROOT_INO
Proof step 30:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs ⊦ files \ orphans(dirs, files) = files \ (orphans(dirs, files) -- m), m = ROOT_INO

Rule argument

pos: right 2

Proof step 17 from proof crash-neutral-evict (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information