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Proof step 1392 from proof inv-renam (previous step)

# links(ino1, dirs) = m3, dirs[ino] = mkdir(m0, md1, # links(ino, dirs), m2, entries1), dirs[ino1] = mkdir(m1, md0, m3, m4, entries0), files[entries0[str]] = mkfile(m, md2, # links(entries0[str], dirs), content0), entries0[str] = entries[str], dirs[ino1] = mkdir(m1, md, m3, m4, entries), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries0[str], md2, false, # links(entries0[str], dirs), 0, m), new_inode = mkinode(ino, md1, true, # links(ino, dirs), m2, m0), old_dent = mkdentry(str, entries0[str]), old_dent_inode = mkinode(entries0[str], md2, false, # links(entries0[str], dirs), 0, m), old_inode = mkinode(ino1, md0, true, m3, m4, m1), 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, md1), pw(user, md0), px(user, md1), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ files, ino ∈ dirs, str ∈ entries, ino = ino1 → md1 = 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)), str0 ∈ entries1, entries0[str] ∈ dirs, q + str ' ⊑ q0 + str0 '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1393:
files[entries[str]] = mkfile(m, md2, # links(entries[str], dirs), content0), dirs[ino1] = mkdir(m1, md, # links(ino1, dirs), m4, entries), dirs[ino] = mkdir(m0, md1, # links(ino, dirs), m2, entries1), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries[str], md2, false, # links(entries[str], dirs), 0, m), new_inode = mkinode(ino, md1, true, # links(ino, dirs), m2, m0), old_dent = mkdentry(str, entries[str]), old_dent_inode = mkinode(entries[str], md2, false, # links(entries[str], dirs), 0, m), old_inode = mkinode(ino1, md, true, # links(ino1, dirs), m4, m1), 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, md), pw(user, md1), px(user, md), px(user, md1), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), ino ∈ dirs, entries[str] ∈ files, ino1 ∈ dirs, str ∈ entries, ¬ entries[str] ∈ dirs, ¬ str0 ∈ entries1, ¬ q + str ' ⊑ q0 + str0 ', ino = ino1 → md1 = md, 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))

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)