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Proof step 6 from proof inv-unlink (previous step)

c_inode.ino = dirs[m].entries[str], c_inode.nlink = files[c_inode.ino].nlink, c_inode.nsubdirs = 0, dent = mkdentry(str, c_inode.ino), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), c_inode.ino ∈ files, str ∈ dirs[m].entries, m ∈ dirs, ¬ c_inode.directory, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_unlink#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
c_inode.ino = entries[str], c_inode.nlink = files[c_inode.ino].nlink, c_inode.nsubdirs = 0, dirs[m] = mkdir(m0, md0, m1, m2, entries), dent = mkdentry(str, c_inode.ino), p_inode = mkinode(m, md, true, m1, m2, m0), afs-cons(dirs, files), m ∈ dirs, str ∈ entries, c_inode.ino ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_unlink#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), c_inode.directory

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, md, 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, md, m1, m2, entries