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Proof step 271 from proof refine-link (previous step)

asynced ↔ bv, dirs[ino2] = mkdir(# entries, md1, # links(ino2, dirs), m3, entries), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), c_inode = getinode(mkdentry(str, entries0[str]).ino, dirs, files), err = err0, err1 = ESUCCESS, err1 = err, err3 = err4, err4 = ESUCCESS, fs = abs-files(files), new_dent = negdentry((q0 + str0 ').last), new_inode = (ino2 ∈ dirs ⊃ mkinode(ino2, md1, true, # links(ino2, dirs), m3, # entries) ;mkinode(ino2, files[ino2].meta, false, files[ino2].nlink, 0, files[ino2].size) ), mkdentry(str, entries0[str]).dentry?, root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md0), px(user, md1), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ files, ino1 ∈ dirs, ino2 ∈ dirs, psynced → asynced0, ⌊err0⌋ ∨ err0 = ESUCCESS, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err1, dirs, files; 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) ∧ err1 = err2)), q0 + str0 ' = ε, root[q + str '].dir?, entries0[str] ∈ dirs, str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 272:
dirs[ino2] = mkdir(# entries, md1, # links(ino2, dirs), m3, entries), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), 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), root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md0), px(user, md1), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ files, ino1 ∈ dirs, ino2 ∈ dirs, ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs, ¬ str0 ∈ entries, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ [afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err, dirs, files; 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))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ p + str ' ≠ ε; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkdentry(str, m).ino = m; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ (p + str ').last = str; (s)