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Proof step 7 from proof crash-neutral-mkdir (previous step)

dent = negdentry(str), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md0, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), m ∈ dirs, ¬ str ∈ dirs[m].entries, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_mkdir#(md; p_inode, c_inode, 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 8:
dirs[m] = mkdir(m0, md1, m1, m2, entries), dent = negdentry(str), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), p_inode = mkinode(m, md0, true, m1, m2, m0), afs-cons(dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_mkdir#(md; p_inode, c_inode, dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), str ∈ 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