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Proof step 10 from proof afs-cons-links-rmorphans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 12:
dirs[m] = mkdir(m0, md, # links(m, dirs), m2, entries), links(m, dirs) = ∅, afs-cons(dirs, files), valid-ino(m, dirs, files), str ∈ entries, m ∈ dirs ⊦ # orphans(dirs, files) = 0, m = ROOT_INO, orphans(dirs, files) = ∅

Rule argument

spec: <toplevel> 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 terms: files, dirs, m