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Proof step 11 from proof crash-neutral-link (previous step)

c_inode = mkinode(dirs[ino].entries[str], md0, false, files[dirs[ino].entries[str]].nlink, 0, m3), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), dirs[ino].entries[str] ∈ files, m ∈ dirs, str ∈ dirs[ino].entries, ino ∈ dirs, ¬ str0 ∈ dirs[m].entries, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
dirs[m] = mkdir(m0, md1, m1, m2, entries), c_inode = mkinode(dirs[ino].entries[str], md0, false, files[dirs[ino].entries[str]].nlink, 0, m3), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, m1, m2, m0), afs-cons(dirs, files), ino ∈ dirs, str ∈ dirs[ino].entries, m ∈ dirs, dirs[ino].entries[str] ∈ files, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO ⊦ ⟨afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), str0 ∈ entries

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m0, md0, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m0, md0, m1, m2, entries