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Proof step 25 from proof crash-neutral-evict (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ino ∈ dirs ∧ ¬ ino ∈ ns → (dirs \ ns)[ino] = dirs[ino]

Rule argument

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

Additional information

Used simplifier rules: ⊦ ino ∈ ns -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ ns; (s) Used terms: ino, orphans(dirs, files) -- m, dirs