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Proof step 60 from proof crash-neutral-evict (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 61:
⊦ (files -- ino) \ ns = (files \ ns) -- ino
Proof step 62:
# links(m, dirs) = 0, files[m] = mkfile(m0, md, 0, content), afs-cons(dirs, files), m ∈ files, ino ∈ files ⊦ m = ROOT_INO, m ∈ dirs, (¬ m ∈ orphans(dirs, files) → ino ≠ m) ∧ (¬ ino ∈ orphans(dirs, files) → files[ino] = ((files \ (orphans(dirs, files) -- m)) -- m)[ino])

Rule argument

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

Additional information

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