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Proof step 605 from proof refine-unlink (previous step)

# links(ino1, dirs) = m1, # entries = m, dirs[ino1] = mkdir(# entries, md, m1, m2, entries), files[entries[str]] = mkfile(m0, md1, # links(entries[str], dirs), content0), entries[str] = entries0[str], dirs[ino1] = mkdir(m, md0, m1, m2, entries0), root.dir?, root[q].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), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino1 ∈ dirs, entries[str] ∈ files, str ∈ entries0, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?; files0 := files; vfs_put_inode#(mkinode(entries[str], md1, false, # links(entries[str], dirs), 0, m0), of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨fs := abs-files(files0); 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)), root[q + str '].dir?, entries[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 606:
⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n, md, n0, n1, entries) → # entries = n
Proof step 607:
⊦ 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 608:
files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content0), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), 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), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?; files0 := files; vfs_put_inode#(mkinode(entries0[str], md1, false, # links(entries0[str], dirs), 0, m0), of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨fs := abs-files(files0); 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) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)