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Proof step 655 from proof inv-renam (previous step)

# links(ino1, dirs) = m4, dirs[entries0[str]] = mkdir(m0, md1, # links(entries0[str], dirs), m3, entries1), dirs[ino1] = mkdir(m2, md0, m4, m5, entries0), dirs[ino] = mkdir(m, md2, # links(ino, dirs), m1, entries2), entries0[str] = entries[str], dirs[ino1] = mkdir(m2, md, m4, m5, entries), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries0[str], md1, true, # links(entries0[str], dirs), 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], md1, true, # links(entries0[str], dirs), m3, m0), old_inode = mkinode(ino1, md0, true, m4, m5, m2), 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, md1), 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 ∈ 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 '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 656:
dirs[ino] = mkdir(m, md2, # links(ino, dirs), m1, entries2), dirs[ino1] = mkdir(m2, md, # links(ino1, dirs), m5, entries), dirs[entries[str]] = mkdir(m0, md1, # links(entries[str], dirs), m3, entries1), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries[str], md1, true, # links(entries[str], dirs), m3, m0), new_inode = mkinode(ino, md2, true, # links(ino, dirs), m1, m), old_dent = mkdentry(str, entries[str]), old_dent_inode = mkinode(entries[str], md1, true, # links(entries[str], dirs), m3, m0), old_inode = mkinode(ino1, md, true, # links(ino1, dirs), m5, m2), entries[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, md1), pw(user, md), px(user, md2), px(user, md), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, entries[str] ∈ dirs, ino1 ∈ dirs, ino ∈ dirs, ¬ str0 ∈ entries2, ¬ q + str ' ⊑ q0 + str0 ', ino = ino1 → md2 = md, 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))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)