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Proof step 1387 from proof inv-renam (previous step)

# links(entries0[str], dirs) = files[entries0[str]].nlink, # links(ino, dirs) = dirs[ino].nlink, # links(ino1, dirs) = dirs[ino1].nlink, entries0[str] = dirs[ino1].entries[str], files[entries0[str]] = mkfile(m1, md1, files[entries0[str]].nlink, content), dirs[ino1] = mkdir(dirs[ino1].size, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries0), dirs[ino] = mkdir(dirs[ino].size, md, dirs[ino].nlink, dirs[ino].nsubdirs, entries), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries0[str], md1, false, files[entries0[str]].nlink, 0, m1), new_inode = mkinode(ino, md, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size), old_dent = mkdentry(str, entries0[str]), old_dent_inode = mkinode(entries0[str], md1, false, files[entries0[str]].nlink, 0, m1), 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), px(user, md0), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), str ∈ dirs[ino1].entries, ino ∈ dirs, entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, ¬ str0 ∈ dirs[ino].entries, ¬ str0 ∈ entries, ¬ entries0[str] ∈ dirs, ¬ q + str ' ⊑ q0 + str0 ', ino = ino1 → md = 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1388:
# links(ino1, dirs) = dirs[ino1].nlink, # links(ino, dirs) = dirs[ino].nlink, # links(entries0[str], dirs) = m0, dirs[ino] = mkdir(dirs[ino].size, md, dirs[ino].nlink, dirs[ino].nsubdirs, entries), dirs[ino1] = mkdir(dirs[ino1].size, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries0), files[entries0[str]] = mkfile(m1, md1, m0, content), entries0[str] = dirs[ino1].entries[str], files[entries0[str]] = mkfile(m, md2, m0, content0), err = ESUCCESS, new_dent = negdentry(str0), new_dent_inode = mkinode(entries0[str], md1, false, m0, 0, m1), new_inode = mkinode(ino, md, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size), old_dent = mkdentry(str, entries0[str]), old_dent_inode = mkinode(entries0[str], md1, false, m0, 0, m1), old_inode = mkinode(ino1, md0, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size), 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, md), pw(user, md0), px(user, md), 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 ∈ dirs[ino1].entries, ino = ino1 → md = 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 ∈ dirs[ino].entries, str0 ∈ entries, entries0[str] ∈ dirs, q + str ' ⊑ q0 + str0 '

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[entries0[str]], m, md2, m0, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[entries0[str]], m, md2, m0, content0