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Proof step 220 from proof refine-unlink (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), files[entries[str]] = mkfile(m, md0, m0, content), dent = mkdentry(str, entries[str]), err = ESUCCESS, fs = abs-files(files), inode = mkinode(ino1, md, true, # links(ino1, dirs), m1, # entries), p_inode = mkinode(entries[str], md0, false, m0, 0, m), 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, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_unlink#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_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)), root[q + str '].dir?, entries[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 221:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), files[entries[str]] = mkfile(m, md0, # links(entries[str], dirs), content), dent = mkdentry(str, entries[str]), err = ESUCCESS, fs = abs-files(files), inode = mkinode(ino1, md, true, # links(ino1, dirs), m1, # entries), p_inode = mkinode(entries[str], md0, false, # links(entries[str], dirs), 0, m), 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, ¬ root[q + str '].dir?, ¬ entries[str] ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_unlink#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_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: 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