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Proof step 238 from proof refine-unlink (previous step)

# entries = m0 + 1, # links(ino1, dirs0) = m2, m0 + 1 = m, dirs0[ino1] = mkdir(m0 + 1, md, m2, m3, entries), files[entries[str]] = mkfile(m1, md1, # links(entries[str], dirs0), content0), entries[str] = entries0[str], dirs0[ino1] = mkdir(m, md0, m2, m3, entries0), fs = abs-files(files), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ entries, ino1 ∈ dirs0, entries[str] ∈ files, str ∈ entries0, dirs ≡ dirs0[ino1, (dirs0[ino1].entries:= (entries0 -- str)).size:= m0], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(ino1, md, true, m2, m3, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries[str], md1, false, # links(entries[str], dirs0), 0, m1); dirs, files); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?; vfs_put_inode#(c_inode, of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1)), entries = ∅, root[q + str '].dir?, entries[str] ∈ dirs0, entries[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 239:
⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n
Proof step 240:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries → (entries[str] ∈ dirs ↔ tree[p + str '].dir?)
Proof step 241:
# entries0 = m0 + 1, files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], dirs0), content0), dirs0[ino1] = mkdir(m0 + 1, md0, # links(ino1, dirs0), m3, entries0), fs = abs-files(files), entries0 ≠ ∅, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files), entries0[str] ∈ files, ino1 ∈ dirs0, str ∈ entries0, dirs ≡ dirs0[ino1, mkdir(m0, md0, # links(ino1, dirs0), m3, entries0 -- str)], ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs0, ¬ entries0[str] ∈ dirs, psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(ino1, md0, true, # links(ino1, dirs0), m3, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md1, false, # links(entries0[str], dirs0), 0, m1); dirs, files); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?; vfs_put_inode#(c_inode, of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err1, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1))

Rule argument

Additional information

Used simplifier rules: make-abs-fold-work: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n;%dir-entry: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries → (entries[str] ∈ dirs ↔ tree[p + str '].dir?);%⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%assign-new-other: ⊦ dirs ≡ dirs0[ino, ad] ∧ ¬ ino0 ∈ dirs0 ∧ ino ∈ dirs0 → ¬ ino0 ∈ dirs; (forward) from specification separation[dir-heap]