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Proof step 15 from proof inv-mkdir (previous step)

# links(m, dirs) = dirs[m].nlink, dirs[m] = mkdir(dirs[m].size, md1, dirs[m].nlink, dirs[m].nsubdirs, entries), dent = negdentry(str), p_inode = mkinode(m, md0, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), ino ≠ 0, afs-cons(dirs, files), m ∈ dirs, ¬ str ∈ dirs[m].entries, ¬ str ∈ entries, ¬ ino ∈ files, ¬ ino ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_mkdir_ino#(m, md, ino; dent, err, dirs)] ( afs-cons(dirs, files) → ⟪afs_inode_sync#(p_inode; dirs, files); p_inode := (p_inode.ino ∈ dirs ⊃ mkinode(p_inode.ino, dirs[p_inode.ino].meta, true, dirs[p_inode.ino].nlink, dirs[p_inode.ino].nsubdirs, dirs[p_inode.ino].size) ;mkinode(p_inode.ino, files[p_inode.ino].meta, false, files[p_inode.ino].nlink, 0, files[p_inode.ino].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟫ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
# links(m, dirs) = m1, dirs[m] = mkdir(m0, md1, m1, m2, entries), dirs[m] = mkdir(m0, md2, m1, m2, entries0), dent = negdentry(str), p_inode = mkinode(m, md0, true, m1, m2, m0), afs-cons(dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_mkdir_ino#(m, md, ino; dent, err, dirs)] ( afs-cons(dirs, files) → ⟪afs_inode_sync#(p_inode; dirs, files); p_inode := (p_inode.ino ∈ dirs ⊃ mkinode(p_inode.ino, dirs[p_inode.ino].meta, true, dirs[p_inode.ino].nlink, dirs[p_inode.ino].nsubdirs, dirs[p_inode.ino].size) ;mkinode(p_inode.ino, files[p_inode.ino].meta, false, files[p_inode.ino].nlink, 0, files[p_inode.ino].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟫ afs-cons(dirs, files)), ino = 0, str ∈ entries0, str ∈ entries, ino ∈ files, ino ∈ dirs

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, entries0]

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, entries0