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Proof step 70 from proof refine-readmeta (previous step)

root[path] = dnode(md1, sdt), ((m => mkdir(# entries, md1, # links(m, dirs), m2, entries) * abs(sdt, entries) * abs|(root, ROOT_INO, path, m)))(dirs), root.dir?, dom of < ino6, fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, path ∈ root, psynced → asynced, m ∈ dirs ∧ m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → dirs[m].entries = ∅, m ∈ dirs → ¬ m ∈ files ∧ dirs[m].nlink = # links(m, dirs) ∧ dirs[m].nlink ≤ 1 ∧ dirs[m].size = # dirs[m].entries ∧ dirs[m].nsubdirs = # subdirs(m, dirs), m ∈ files → ¬ m ∈ dirs ∧ files[m].nlink = # links(m, dirs), ∀ ino. (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE), ∀ name. m ∈ dirs ∧ name ∈ dirs[m].entries → dirs[m].entries[name] ∈ dirs ∨ dirs[m].entries[name] ∈ files, ∀ n. m ∈ files ∧ n ∈ files[m].content → # files[m].content[n] = VFS_PAGE_SIZE ⊦ m2 = # dnode(md1, sdt).subdirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
dirs[m].nlink = # links(m, dirs), dirs[m].nsubdirs = # subdirs(m, dirs), dirs[m].size = # dirs[m].entries, root[path] = dnode(md1, sdt), ((m => mkdir(# entries, md1, # links(m, dirs), m2, entries) * abs(sdt, entries) * abs|(root, ROOT_INO, path, m)))(dirs), root.dir?, dom of < ino6, fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, path ∈ root, # links(m, dirs) ≤ 1, m ≠ ROOT_INO ∧ links(m, dirs) = ∅ → dirs[m].entries = ∅, psynced → asynced, ∀ ino. (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅) ∧ ( ino ∈ dirs → ¬ ino ∈ files ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ files[ino].nlink = # links(ino, dirs)) ∧ (∀ name. ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ (∀ n. ino ∈ files ∧ n ∈ files[ino].content → # files[ino].content[n] = VFS_PAGE_SIZE), ∀ name. name ∈ dirs[m].entries → dirs[m].entries[name] ∈ dirs ∨ dirs[m].entries[name] ∈ files ⊦ m2 = # dnode(md1, sdt).subdirs, m ∈ files

Rule argument

Additional information

Used simplifier rules: path-in-end: ⊦ ispath(p, n, m, dirs, files) ∧ ¬ m ∈ files → m ∈ dirs; (forward) from specification afs-base% ⊦ ((ino => ad * D))(dirs) → ino ∈ dirs; (s)%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]