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Proof step 47 from proof crash-neutral-evict (previous step)

# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files ⊦ m = ROOT_INO, m ∈ dirs, dirs \ orphans(dirs, files) = dirs \ (orphans(dirs, files) -- m) ∧ files \ orphans(dirs, files) = (files -- m) \ (orphans(dirs, files) -- m)

User applied rule case distinction

And obtained the following new goals

Proof step 48:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files ⊦ dirs \ orphans(dirs, files) = dirs \ (orphans(dirs, files) -- m), m = ROOT_INO, m ∈ dirs
Proof step 55:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files ⊦ files \ orphans(dirs, files) = (files -- m) \ (orphans(dirs, files) -- m), m = ROOT_INO, m ∈ dirs

Rule argument

pos: right 3

Proof step 47 from proof crash-neutral-evict (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information