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Proof step 565 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), c_inode = inode, dent = negdentry(dent0.name), dent0 = negdentry(str), err = ENOENT, err1 = err, err2 = ESUCCESS, fs = abs-files(files), inode = (ino1 ∈ dirs ⊃ mkinode(ino1, md, true, # links(ino1, dirs), m1, # entries) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ), p_ino = ino1, 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), pre-lookup(p_ino, dent0, dirs, files), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced ⊦ ⟨posix_link#(q + str ', path', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0), path' = ε, dent0.name ∈ dirs[p_ino].entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 566:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), path' ≠ ε, 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), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, ¬ str ∈ entries, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_link#(q + str ', path', user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOENT = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ negdentry(str).name = str; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ pre-lookup(p_ino, dent, dirs, files) ↔ valid-parent-ino(p_ino, dirs, files); (s)