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Proof step 18 from proof crash-neutral-evict (previous step)

# 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ (dirs -- ino) \ ns = (dirs \ ns) -- ino
Proof step 20:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, ∅), afs-cons(dirs, files), m ∈ dirs ⊦ dirs \ orphans(dirs, files) = (dirs \ (orphans(dirs, files) -- m)) -- m, m = ROOT_INO

Rule argument

spec: heap, inst: dir-heap name: diffs-sw seq: ⊦ (dirs -- ino) \ ns = (dirs \ ns) -- ino subst: [ns, ino, dirs] → [orphans(dirs, files) -- m, m, dirs] flags: <all paths>

Additional information

Used terms: orphans(dirs, files) -- m, m, dirs