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Proof step 21 from proof afs-cons-rename-dir-dentry (previous step)

dirs[m] = mkdir(m2, md4, # links(m, dirs), m5, entries), dirs[entries[str]] = mkdir(m1, md3, # links(entries[str], dirs), m3, ∅), dirs[dirs[m0].entries[str0]] = mkdir(m4, md5, # links(dirs[m0].entries[str0], dirs), m7, entries0), new_child_inode = mkinode(entries[str], md, true, # links(entries[str], dirs), m3, m1), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md1, true, # links(m, dirs), m5, m2), old_child_inode = mkinode(dirs[m0].entries[str0], md0, true, # links(dirs[m0].entries[str0], dirs), m7, m4), old_dent = mkdentry(str0, dirs[m0].entries[str0]), old_parent_inode = mkinode(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), entries[str] ≠ ROOT_INO, afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, dirs[m0].entries[str0] ∈ dirs, entries[str] ∈ dirs, str0 ∈ dirs[m0].entries, str ∈ entries, m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
dirs[entries1[str0]] = mkdir(m4, md5, # links(entries1[str0], dirs), m7, entries0), dirs[entries[str]] = mkdir(m1, md3, # links(entries[str], dirs), m3, ∅), dirs[m] = mkdir(m2, md4, # links(m, dirs), m5, entries), dirs[m0] = mkdir(m6, md6, m8, m9, entries1), new_child_inode = mkinode(entries[str], md, true, # links(entries[str], dirs), m3, m1), new_dent = mkdentry(str, entries[str]), new_parent_inode = mkinode(m, md1, true, # links(m, dirs), m5, m2), old_child_inode = mkinode(entries1[str0], md0, true, # links(entries1[str0], dirs), m7, m4), old_dent = mkdentry(str0, entries1[str0]), old_parent_inode = mkinode(m0, md2, true, m8, m9, m6), afs-cons(dirs, files), str ∈ entries, str0 ∈ entries1, entries[str] ∈ dirs, entries1[str0] ∈ dirs, m ∈ dirs, m0 ∈ dirs, m = m0 → md1 = md2, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), entries[str] = ROOT_INO

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[m0], m6, md6, m8, m9, entries1]

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[m0], m6, md6, m8, m9, entries1