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Proof step 364 from proof refine-link (previous step)

dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), files0[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), entries0[str] = entries[str], dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), files = files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)], ino = inode.ino, inode = mkinode(entries0[str], md2, false, # links(entries0[str], dirs0), 0, m0), root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md), px(user, md0), px(user, md), px-parent(user, q0, ROOT_INO, dirs0, files0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, entries[str] ∈ files0, ino1 ∈ dirs0, ino3 ∈ dirs0, str ∈ entries, ino2 ∈ dirs0, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ [c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, abs-files(files0), abs-of(of); err2, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), root[q + str '].dir?, ino ∈ files, entries[str] ∈ dirs0, str0 ∈ entries1, ino ∈ dirs

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)%⊦ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) → abs-files(files[ino, mkfile(m, md, n1, content)]) = abs-files(files); (s)%path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs; (forward) from specification afs-base