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Proof step 411 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino2] = mkdir(# entries, md1, # links(ino2, dirs), m3, entries), c_inode = mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m), err = ESUCCESS, fs = abs-files(files), new_dent = negdentry(str0), new_inode = mkinode(ino2, md1, true, # links(ino2, dirs), m3, # entries), old_dent = mkdentry(str, entries0[str]), p_inode = new_inode, root[q0].dir?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), ispath(q0, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files), pw(user, md1), px(user, md1), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), ino2 ∈ dirs, ino1 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, psynced → asynced0, links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, fs, abs-of(of); err2, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), root[q + str '].dir?, entries0[str] ∈ dirs, str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 412:
# links(entries0[str], dirs) = files[entries0[str]].nlink, # entries = dirs[ino2].size, # links(ino2, dirs) = dirs[ino2].nlink, entries0[str] = dirs[ino].entries[str], dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), files[entries0[str]] = mkfile(m, md, files[entries0[str]].nlink, content), dirs[ino2] = mkdir(# entries, md1, dirs[ino2].nlink, dirs[ino2].nsubdirs, entries), root[q0].dir?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), ispath(q0, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md1), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, q0, ROOT_INO, dirs, files), str ∈ dirs[ino].entries, ino ∈ dirs, ino2 ∈ dirs, ino1 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, ¬ root[q + str '].dir?, ¬ str0 ∈ dirs[ino2].entries, ¬ entries0[str] ∈ dirs, ¬ str0 ∈ entries, psynced → asynced0, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟨posix_link#(q + str ', q0 + str0 ', user, abs-files(files), abs-of(of); err2, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ negdentry(str).negdentry?; (s)% ⊦ negdentry(str).name = str; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)%⊦ valid-dentry(dent, dirs, files) ↔ (∃ ino. valid-dentry(ino, dent, dirs, files)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, dirs, files) ↔ valid-dentry(old_dent, dirs, files) ∧ valid-negdentry(p_inode.ino, new_dent, dirs, files) ∧ (links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO) ∧ valid-dir-inode(p_inode, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ c_inode.ino = old_dent.ino; (s)