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Proof step 28 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, m ∈ orphans(dirs, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: afs-base name: orphans seq: ⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO subst: [files, dirs, ino] → [files, dirs, m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set] Used terms: files, dirs, m