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Proof step 652 from proof inv-renam (previous step)

# links(entries0[str], dirs) = dirs[entries0[str]].nlink, # links(ino1, dirs) = dirs[ino1].nlink, entries0[str] = dirs[ino1].entries[str], dirs[ino] = mkdir(m, md2, # links(ino, dirs), m1, entries2), dirs[ino1] = mkdir(dirs[ino1].size, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries0), dirs[entries0[str]] = mkdir(dirs[entries0[str]].size, md, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, entries), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries0[str], md, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size), new_inode = mkinode(ino, md2, true, # links(ino, dirs), m1, m), old_dent = mkdentry(str, entries0[str]), old_dent_inode = mkinode(entries0[str], md, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size), old_inode = mkinode(ino1, md0, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size), entries0[str] ≠ ROOT_INO, dom of < ino2, afs-cons(dirs, files), ispath(q0, ROOT_INO, ino, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md2), pw(user, md), pw(user, md0), px(user, md2), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ dirs[ino1].entries, str ∈ entries0, entries0[str] ∈ dirs, ino1 ∈ dirs, ino ∈ dirs, ¬ str0 ∈ entries2, ¬ q + str ' ⊑ q0 + str0 ', ino = ino1 → md2 = md0, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err, dirs, files; asynced)] (afs-cons(dirs, files) → ⟪skip⟫ of-cons(of, dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 653:
# links(ino1, dirs) = dirs[ino1].nlink, # links(entries0[str], dirs) = m2, dirs[entries0[str]] = mkdir(m0, md, m2, m3, entries), dirs[ino1] = mkdir(dirs[ino1].size, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries0), dirs[ino] = mkdir(m, md2, # links(ino, dirs), m1, entries2), entries0[str] = dirs[ino1].entries[str], dirs[entries0[str]] = mkdir(m0, md1, m2, m3, entries1), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries0[str], md, true, m2, m3, m0), new_inode = mkinode(ino, md2, true, # links(ino, dirs), m1, m), old_dent = mkdentry(str, entries0[str]), old_dent_inode = mkinode(entries0[str], md, true, m2, m3, m0), old_inode = mkinode(ino1, md0, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size), dom of < ino2, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), ispath(q0, ROOT_INO, ino, dirs, files), of-cons(of, dirs, files), pw(user, md0), pw(user, md), pw(user, md2), px(user, md0), px(user, md2), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), ino ∈ dirs, ino1 ∈ dirs, entries0[str] ∈ dirs, str ∈ entries0, str ∈ dirs[ino1].entries, ino = ino1 → md2 = md0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ [afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err, dirs, files; asynced)] (afs-cons(dirs, files) → ⟪skip⟫ of-cons(of, dirs, files)), entries0[str] = ROOT_INO, str0 ∈ entries2, q + str ' ⊑ q0 + str0 '

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[entries0[str]], m0, md1, m2, m3, 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[entries0[str]], m0, md1, m2, m3, entries1